• Notation

Motivations

Prelims

Boring setup

Sequences of Sets

Probability Spaces

We introduce the idea of measure as a system of ”consistent allocation” under partitioning. This will be used in the algebra of probability spaces.

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Measure Theory Setup

• Why go through this pain
• Intuition to carry: “Conservation of stuff”

$\sigma$-Algebras

Measure Space

Structure of Measure

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Probability Spaces

Sources

theanalysisofdata.com/probability

Random: Probability, Mathematical Statistics, Stochastic Processes

Books

measure theory

Measure, Integration & Real Analysis

easier