probability space

definition

A probability space is simply a measure space where the measure of the whole space is one (i.e. .)

• (the set) is the sample space
• is called an event
• (the measure) is called the probability of A.

Notes:

This captures a lot of intuition about probability.

• Notice that by the definition of measure.
• Disjoint additivity holds… so having more things that are considered a success for an event will increase the probability.
• Every event’s complement is in the -algebra and