Lebesgue measurable

Intuition

Kind of what is sounds like… a set that can be measured by the Lebesgue measure. However, it is not just the sets in the 20231218115557-borel_sigma_algebra, but it is up to null sets.

Formal definition

A set $A\subseteq \mathbb{R}$ is Lebesgue measurable if $\exists B\subseteq A$ such that $|A\backslash B|=0$

Notes

Sets that are Lebesgue sets and not Borel sets are really hard to find.