Notes on book "Measure Theory (2nd ed.) - Cohn Donald L."

Measure Thoery: Chp 8. Polish Spaces and Analytic Sets

Polish Spaces

A Polish space is a separable topological space that can be metrized using a complete metric.

Analytic Sets

Let be a Polish space. A subset of is analytic if there is a Polish space and a continuous function such that .

The Separation Theorem and Its Consequences

Theorem 8.3.1. Let be a Polish space, and let and be disjoint analytic subsets of . Then and can be separated by Borel sets.

References

[1] @book{cohn2013measure, title={Measure theory}, author={Cohn, Donald L}, year={2013}, publisher={Springer} }