Τομέας Μαθηματικής Ανάλυσης
Library of the School of Science

2012-02-29

2012

Δημητρίου Ξενοφών

Αν.Καθηγητής Νικόλαος Παπαναστασίου

Συγκλίσεις ακολουθιών μέτρων και μετρήσιμων συναρτήσεων

Greek

In this dissertation we introduce new notions of convergence of measure
sequences and using them we strengthen and extend classical limit theorems of
Measure Theory like the theorems of Nikodym, Brooks – Jewett, Vitali – Hahn –
Saks and Schur.
Moreover we define and study new notions of convergence for sequences
of measurable functions which are weaker than the classical convergence in
measure. Using these we prove new density theorems in IR. We consider the modes
of convergence mentioned in the dissertation to be useful in the research in
Probability Theory (e.g. in the study of ultra – weak laws of large numbers),
in Topology (e.g. in the study of density topologies) and in Functional
Analysis (e.g. in the study of function spaces of Baire – type and Ascoli –
type theorems).

Cos – convergence, Complete convergence, Exhaustiveness, Weak exhaustiveness, Ideal limits

No

0

No

133

215

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https://pergamos.lib.uoa.gr/uoa/dl/object/1309341