An important note for ergodic theory

Algebra, sigma algebra, and topological space

The following definitions helped me getting started with ergodic theory. Hahn Kolmogorov Extension theorem and everything else starts with a proper understanding of the Algebra, sigma algebra and topological space and techniques to transport from one to the other.

‘An algebra is a collection of subsets closed under finite unions and intersections. A sigma algebra is a collection closed under countable unions and intersections. In either case, compliments are also included. A topologist believes certain sets are open. It should include all unions. But, open set collection needs to be closed only under intersections of a finite number of subsets.’


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