# Set Theory * A **set** is a collection of **elements** * A **space** is a collection of all elements under consideration There are 3 natural operations on sets: 1. **Complement** 2. **Union** 3. **Intersection** The **Powerset** is the collections of all sets in a space, $X$. The powerset has certain pathologies that make it undesirable to work with. We wish to work with a restriction of the power set that is closed under the three set operations. A restricted collection of sets satisfying the closure properties is a **sigma algebra**. It is referred to as a sigma algebra over the space X. --- Date: 20220713 Links to: Tags: #review References: * [Betancourt, probability (see notabillity annotations)](https://betanalpha.github.io/assets/case_studies/probability_theory.html)