🧠📚 Mitch's Mind Tangle

Search

SearchSearch
      • cone over space
      • constant rank theorem
      • equivariant rank theorem
      • fixed point set
      • frontier condition
      • locally finite decomposition
      • orbit type stratification
      • principal orbit type theorem
      • proper group action
      • stratified symplectic space
      • stratified topological space
      • cotangent lift
      • de Rham cohomology
      • de Rham theorem
      • integral of differential form
      • Stokes theorem
      • symplectic volume
      • tautological form
        • ACE simulation with subjective prices
        • Carry charge hedge
        • Finance
        • OHMC with Approx Bayesian Comp
        • Pure risk avoidance hedging
        • Risk neutral density
        • Stacked synthetic storage strategy
        • Subjective asset pricing
        • subjective distribution
        • Subjective OHMC
        • synthetic refining strategy
        • Synthetic storage strategy
      • Austrian economics
      • choice architecture active inference
      • communication system advances human knowlege
      • dynamic choice set
      • Economics
      • Efficient Market Hypothesis
      • entrepreneurship adoption and state space
      • entrepreneurship and active inference
      • models and knowledge
      • Neoclassical Equilibrium
      • Problems with utility based choice models
      • Society members as observations
      • 10: The Market Order or Catallaxy
      • A step-by-step tutorial on active inference and its application to empirical data
      • Active inference and agency: optimal control without cost functions
      • Active inference: The free energy principle in mind, brain, and behavior
      • Algebra: Chapter 0
      • Algebraic topology
      • An introduction to Bayesian network theory and usage
      • An Introduction to the Bootstrap
      • Analysis of integrated and cointegrated time series with R
      • Bayesian Model Comparison and Validation
      • Bayesian networks: An introduction
      • Bayesian Specification Analysis in Econometrics
      • Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician
      • Chapter 2: The Low Road to Active Inference
      • De Finetti was Right: Probability Does Not Exist
      • Economics and knowledge
      • Entrepreneurship and economic growth: The theory of emergent institutions.
      • Foundations of mechanics
      • Gelfand–Cetlin abelianizations of symplectic quotients
      • Hedge your monte carlo
      • Hedging in the theory of corporate finance: A reply to our critics
      • How to take smart notes: One simple technique to boost writing, learning and thinking
      • Insurance: Don't Sweat the Small Stuff
      • Introduction to Modern Bayesian Econometrics
      • Introduction to smooth manifolds
      • Introduction to smooth manifolds
      • Introduction to symplectic topology
      • Keynote: Dr. Stephen Wolfram
      • Lack of confidence in approximate Bayesian computation model choice
      • Learning, estimation, and the stability of rational expectations
      • Lectures on poisson geometry
      • Lectures on symplectic geometry
      • Market Models: A Guide to Financial Data Analysis
      • Mathematical Statistics and Data Analysis
      • Measure, integration & real analysis
      • METALLGESELLSCHAFT AND THE ECONOMICS OF SYNTHETIC STORAGE
      • Nudge: The final edition
      • Numbers as a cognitive and social technology: on the nature of conventional number sequences used in economic systems
      • On Discriminative vs. Generative Classifiers: A comparison of logistic regression and naive Bayes
      • Probabilistic Graphical Models: Principles and Applications
      • Representations of compact lie groups
      • Retrospect and Prospect
      • Riemannian geometry
      • Risk transfer: derivatives in theory and practice
      • Stratified symplectic spaces and reduction
      • Symposium on current views of subjective probability: Subjective probability as the measure of a non-measurable set
      • The local structure of Poisson manifolds
      • The math is not the territory: navigating the free energy principle
      • Topics in differential geometry
      • Value at Risk: Uses and Abuses
      • What Should Economists Do?
      • (left) resolution of R-module
      • (local) coframe
      • (local) frame
      • $\sigma$-algebra
      • $\sigma$-algebra closed under countable intersection
      • 1-parameter subgroup
      • abelian group
      • action
      • action of fundamental group on cover
      • action-angle coordinates
      • adjoint representation of Lie algebra
      • adjoint representation of Lie group
      • affine algebraic group
      • affine algebraic variety
      • affine connection
      • algebra homomorphism
      • algebra ideal
      • algebra of invariants
      • algebraic geometry
      • algebraic structures
      • algebraic topology
      • algebraically closed field
      • annihilator of module
      • annihilator of vector space
      • approximation by simple functions
      • associative algebra
      • basis for exterior product
      • basis for tangent space of manifold
      • Bolzano-Weierstrass Theorem
      • Borel $\sigma$ algebra
      • Borel measurable function
      • boundary of chain complex
      • boundary of set
      • bounded convergence theorem
      • Cartan's magic formula
      • categorical quotient
      • category
      • category theory
      • Cayley-Hamilton theorem
      • chain complex
      • chain homotopy
      • chain map
      • characteristic polynomial
      • chart
      • Christoffel symbol
      • class
      • classical analysis
      • closed subgroup theorem
      • closure of set
      • cofinite topology
      • coisotropic subspace
      • commuting vector fields
      • compact space
      • complete vector field
      • completely integrable system
      • conformal metric
      • continuity with limsup
      • continuous functions and basis
      • continuous map
      • cotangent bundle
      • cotangent space
      • covering space
      • cumulative distribution function
      • curve
      • cycle of chain complex
      • cyclic module
      • Darboux thoerem
      • De Morgan's law
      • defining map
      • deformation retract
      • density function
      • derivation
      • diffeomorphism
      • differences between Riemann and Lebesgue integral
      • differential
      • differential form
      • differential geometry
      • direct product (groups)
      • direct sum
      • Directed acyclic graph (DAG)
      • Dirichlet function
      • discrete topology
      • distribution of random variable
      • division ring
      • domain (algebra)
      • domain (ring theory)
      • dominated convergence theorem
      • dual basis
      • dual space
      • effective action
      • Egorov's Theorem
      • embedded submanifold
      • equivalent categories
      • equivariant map
      • equivariant map
      • essentially surjective
      • Euclidean topology
      • exact complex
      • exact sequence
      • excision theorem
      • expected value
      • exponent of module
      • exponential map
      • extension module
      • exterior algebra
      • exterior derivative
      • exterior power
      • faithful functor
      • fiber bundle
      • field
      • field of fractions
      • finite complement topology
      • finitely generated algebra
      • first isomorphism theorem
      • flat R-module
      • flow
      • foliation
      • free group
      • free group action
      • free product (groups)
      • free R-module
      • free resolution
      • Frobenius theorem
      • full functor
      • functor
      • fundamental group
      • Fundamental Theoreom on Flows
      • fundamental vector fields
      • general linear group
      • generalized orthogonal group
      • generated submodule
      • graded abelian group
      • graded algebra
      • graded ring
      • graph
      • group
      • group action
      • group homomorphism
      • group representation
      • group ring
      • Group theory
      • Hamiltonian action
      • Hamiltonian G-space
      • Hamiltonian torus actions and integrable systems
      • Hamiltonian vector field
      • Hausdorff space
      • Hilbert Basis Theorem
      • Hilbert's finiteness theorem
      • homeomorphism
      • homogeneous space
      • homology
      • homotopy
      • homotopy equivalence
      • homotopy equivalent complexes
      • homotopy group
      • Hurewicz theorem
      • ideal (ring theory)
      • immersion
      • Implicit function theorem
      • independence (probability)
      • induced measure
      • induced Riemannian metric
      • induced subgroup from cover
      • infinitesimal generator
      • inner product
      • integral curve
      • integral leaks
      • integral manifold
      • interior of set
      • interior product
      • invariant function
      • invariant subset
      • Inverse function theorem
      • involutive distribution
      • irreducible representation
      • isomorphism
      • isotropic subspace
      • Jacobson radical
      • Jordan canonical form
      • Kolmogorov's 0-1 law
      • Lagrangian subspace
      • Lebesgue integrability
      • Lebesgue integral
      • Lebesgue measurable
      • Lebesgue measure
      • Lebesgue number lemma
      • left-invariant vector field
      • level set
      • Levi-Civita connection
      • Lie algebra
      • Lie algebra action
      • Lie algebra of a Lie group
      • Lie algebra representation
      • Lie bracket
      • Lie derivative
      • Lie group
      • Lie group representation
      • Lie theory
      • Lie's third theorem
      • lifting criterion for continuous maps
      • linear algebra
      • linear symplectomorphism
      • local ring
      • localization at a prime ideal
      • localization of a module
      • localization of a ring
      • locally free
      • long exact sequence of homology
      • loop
      • lower Lebesgue sum
      • lower limit topology
      • Luzin's Theorem
      • Marsden-Weinstein symplectic reduction theorem
      • Math
      • matrix exponential
      • matrix Lie algebra
      • maximal ideal
      • maximal smooth atlas
      • maximal spectrum
      • Mayer-Vietoris Theorem
      • measure
      • measure space
      • Measure theory
      • measureable function
      • metric
      • metric topology
      • minimal polynomial
      • module over ring
      • moment map
      • Monotone Convergence Theorem
      • monotone convergence theorem (integral version)
      • multi-vector fields
      • multiplicative subset
      • multiplicity of representation
      • Nakayama's Lemma
      • natural transformation
      • nested interval theorem
      • Noetherian R-module
      • Noetherian ring
      • not Lebesgue integrable function
      • not Riemann integrable function
      • open map
      • orbit
      • orbit space
      • orbits as submanifolds
      • orthogonal group
      • outer measure
      • partition of unity
      • path
      • path lifting lemma
      • period (of module)
      • PID modules
      • Poincare lemma
      • Poisson algebra
      • Poisson bracket
      • Poisson bracket on symplectic manifold
      • Poisson commute
      • Poisson manifold
      • Poisson map
      • polynomial ring
      • presentation of a group
      • prime ideal
      • principal bundle
      • principal ideal domain
      • probability space
      • Probability theory
      • projective R-module
      • projective resolution
      • proper map
      • quaternions
      • quotient group
      • quotient manifold theorem
      • quotient map
      • quotient ring
      • quotient topology
      • R-algebra
      • R-module
      • radical of an ideal
      • random variable
      • rank of smooth map
      • rational canonical form
      • reduced homology
      • reduced ring
      • regular
      • regular cover
      • regular distribution
      • regular value
      • regular value theorem
      • related vector fields
      • relative singular homology
      • representation theory
      • retract
      • Ricci curvature tensor
      • Riemann curvature
      • Riemann integrability
      • Riemann integral
      • Riemann lower/ upper sum
      • Riemannian metric
      • ring
      • scalar curvature
      • Schouten bracket
      • Schur's Lemma
      • second countable
      • section
      • sectional curvature
      • Seifert-Van Kampen Theorem
      • semilocally simply connected
      • short exact sequence
      • simple function
      • simple graph
      • simple module
      • simplex
      • simply connected space
      • singular distribution
      • singular homology
      • singular point
      • singular value
      • skeleton
      • slice chart
      • smallest $\sigma$-algebra
      • smooth bump function
      • smooth embedding
      • smooth function
      • smooth manifold
      • smooth map
      • space of all vector fields
      • special linear group
      • stabilizer
      • stereographic projection
      • stock
      • submersion
      • subspace topology
      • symmetric power
      • symplectic action
      • symplectic complement
      • symplectic geometry
      • symplectic group
      • symplectic leaf
      • symplectic manifold
      • symplectic vector field
      • symplectic vector space
      • symplectic vector subspace
      • symplectomorphism
      • tail field
      • tangent bundle
      • tangent space
      • tensor coordinate matrix
      • tensor field
      • tensor product
      • tensor rank
      • topological basis
      • topological embedding
      • topological group
      • topological manifold
      • topological pair
      • topology
      • topology generated by basis
      • Tor group
      • torsion (module theory)
      • torsion of affine connection
      • torus (topology)
      • trace
      • transitive group action
      • unitary group
      • universal cover
      • universal cover criterion
      • vanishing locus
      • vector bundle
      • vector field
      • vector space
      • vector space as a k-module
      • vector space as an affine variety
      • velocity vector of curve
      • Vitali set
      • Weak product (group)
      • Weinstein splitting theorem
      • Zariski topology
      • affine scheme
      • algebraic closure
      • algebraic extension
      • algebraic numbers
      • Artin-Wedderburn theorem
      • bimodule
      • center of a ring
      • character of group representation
      • class function
      • commutator subgroup
      • coordinate ring
      • degree of extension
      • equivalence of reduced algebras and affine sets
      • field characteristic
      • field extension
      • finitely generated extension
      • idempotent
      • injective R-module
      • inverse limit
      • Maschke lemma
      • module on sheaf
      • nilradical of ring
      • normal subgroup
      • Nullstellensatz
      • opposite category
      • opposite ring
      • orthogonal family of central idempotents
      • partially ordered set
      • prime spectrum
      • prime subfield
      • representation theory of finite groups
      • ringed space
      • semisimple module
      • semisimple ring
      • sheaf
      • simple field extension
      • skyscraper sheaf
      • weak Nullstellensatz
      • Zariski's Lemma
      • Zorn's lemma
      • bialgebra
      • coalgebra
      • Poincare-Birkhoff-Witt theorem
      • tensor algebra
      • universal enveloping algebra
        • 2 model posterior odds
        • Approximate Bayesian Computation (ABC)
        • Bayes Factor
        • Bayes net criteria
        • Bayesian interval and non-measureable
        • Bayesian network
        • Bayesian network joint probability
        • Bayesian prediction algorithm
        • Bayesian Specification Test
        • Bayesian statistics
        • Bayesian surprise
        • Honesty of Bayesian inference
        • Likelihood ratio - frequentist
        • Likelihood ratio vs. Bayes factor
        • MC and BN
        • Posterior odds on a model
        • Posterior prediction vs. parametric bootstrap
        • Posterior Predictive Distribution
        • Predictive distribution
        • Simulating distribution
        • Simulating sample predictions from test data
        • AR time series model
        • ARMA time series models
        • Autocovariance
        • detrending series
        • integrated process
        • MA time series
        • Mean reversion
        • Second Order Stationary
        • stability of VAR model
        • Stationary time series
        • Trend-stationary process
        • VAR model
        • VAR model
        • VECM - time series
      • active inference in behavioral economics
      • conditional independence
      • Convergence of stationary MC
      • Criticisms of MLE
      • Discriminative model
      • expected free energy
      • generative model
      • graph of HMM
      • Hidden Markov Model (HMM)
      • Markov chain
      • Markov chain matrix
      • Markov property
      • Maximum Likelihood Estimator (MLE)
      • Monte Carlo Markov chain
      • Parametric Bootstrap
      • Probabilistic Graphical Model (PGM)
      • rejection sampling
      • Stationary MC distribution
      • Statistics
      • surprise (statistical)
      • variational free energy
      • Connection is crucial
      • reading as a process
    Home

    ❯

    Math

    ❯

    Lebesgue measure

    Lebesgue measure

    May 16, 20251 min read

    • definition

    Lebesgue measure

    The Lebesgue measure is nothing more than the outer measure when restricted to the 20231218115557-borel_sigma_algebra or the Lebesgue sigma algebra.

    Graph View

    Backlinks

    • Lebesgue measurable
    • not Lebesgue integrable function

    Created with Quartz v4.2.3 © 2025

    • GitHub
    • Discord Community