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Identifier

000451314

Title

Η μετρησιμότητα των αναλυτικών συνόλων

Alternative Title

The measurability of analytical sets

Author

Νταβιγλάκης, Γιάννης

Thesis advisor

Μήτσης Θεμιστοκλής

Reviewer

Φραντζικινάκης, Ν.
Παπαδημητράκης, Μ.
Μήτσης, Θ.

Abstract

In this thesis, we deal with some properties (related to topology and measure theory) that the Borel subsets of a complete and separable metric space possess. The thesis is divided into four sections: In the first section, we deal with some examples and properties (mostly related to measure theory) of complete and separable metric spaces. In the second section, we introduce the concept of “analytic” sets. They are the most “normal” subsets of a complete and separable metric space, second only to the Borel subsets. The section contains some examples and properties of analytic sets as well as an example of an analytic set that is not a Borel. In the third section, we provide some additional properties of analytic sets (as consequences of a seperation theorem) and we prove a theorem that associates the cardinality of two Borel subsets of complete, separable metric spaces with the existence of a Borel isomorphsim between them. Finally, in the fourth section, we prove the main result of this thesis, which is the measurability of analytic sets with respect to every finite Borel measure in a separable and complete metric space.

Language

Greek, English

Subject

Polish spaces

Issue date

2022-07-22

Collection

School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses

Type of Work--Post-graduate theses

Permanent Link

https://elocus.lib.uoc.gr//dlib/5/6/5/metadata-dlib-1664345035-923075-3948.tkl