Borel Algebra, Borel functions (part 1) | Intersection of sigma algebras is also sigma algebra

In this series of two video tutorials you will learn Borel algebra and Borel functions. I will prove that intersection of sigma algebras is also sigma algebra. Then I will define what is a generator system and minimal sigma-algebra and how it can be constructed. Then we will define Borel algebra and Borel sets. Next I will prove criterion of the function being measurable in terms of Borel sets and Borel algebra. This result will be used in the proof of the fact that composition of Borel and Measurable functions is Measurable function.