Post-graduate theses
Current Record: 31 of 127
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Identifier |
000451314 |
Title |
Η μετρησιμότητα των αναλυτικών συνόλων |
Alternative Title |
The measurability of analytical sets |
Author
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Νταβιγλάκης, Γιάννης
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Thesis advisor
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Μήτσης Θεμιστοκλής
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Reviewer
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Φραντζικινάκης, Ν.
Παπαδημητράκης, Μ.
Μήτσης, Θ.
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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.
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Language |
Greek, English |
Subject |
Polish spaces |
Issue date |
2022-07-22 |
Collection
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School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
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Type of Work--Post-graduate theses
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Permanent Link |
https://elocus.lib.uoc.gr//dlib/5/6/5/metadata-dlib-1664345035-923075-3948.tkl
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Views |
312 |