# Probability Theory Formal probability theory works with **sets** in a given **space**, so we must start with a very brief overview of set theory. ### Set Theory A **set** is a collection of elements and a **space** is the collection of all elements under consideration. There are three natural operations that arise between sets: *set complement,* *set union*, and *set intersection*. The collection of all sets in a space, $X$, is called the **power set**, $P(X)$. A **sigma algebra** TODO: continue --- Date: 20220522 Links to: Tags: #review References: * Notability, Probability Theory * [Probability Theory (For Scientists and Engineers)](https://betanalpha.github.io/assets/case_studies/probability_theory.html)