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On some problems in set-theoretic re...

Kumar, Ashutosh.

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On some problems in set-theoretic real analysis.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	On some problems in set-theoretic real analysis./
Author:	Kumar, Ashutosh.
Description:	41 p.
Notes:	Source: Dissertation Abstracts International, Volume: 75-08(E), Section: B.
Contained By:	Dissertation Abstracts International75-08B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3620124
ISBN:	9781303898280

On some problems in set-theoretic real analysis.
Kumar, Ashutosh.

On some problems in set-theoretic real analysis. - 41 p.

Source: Dissertation Abstracts International, Volume: 75-08(E), Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2014.

This thesis contains a few applications of set-theoretic methods to certain problems in real analysis. In the first two sections of Chapter 1, we discuss some results related to a question of Fremlin about partitions of a set of reals into null sets. In Section 3, we answer a questions of Komjath in dimension one. Our proof uses some results of Gitik and Shelah in an essential way. In Chapter 2, we answer a couple of questions about finitely additive total extensions of Lebesgue measure. These problems arose from a question of Juhasz in set-theoretic topology. In Chpater 3, we give some "natural" examples of additive subgroups of reals of arbitrarily high finite Borel rank. The existence of such groups is an old and well known result. In Chapter 4, we construct a non principal ultrafilter from any free maximal ideal in the ring of bounded continuous functions on reals.

ISBN: 9781303898280Subjects--Topical Terms:

515831
Mathematics.

On some problems in set-theoretic real analysis.
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020 $a 9781303898280
035 $a (MiAaPQ)AAI3620124
035 $a AAI3620124
040 $a MiAaPQ $c MiAaPQ
100 1 $a Kumar, Ashutosh. $3 2101075
245 1 0 $a On some problems in set-theoretic real analysis.
300 $a 41 p.
500 $a Source: Dissertation Abstracts International, Volume: 75-08(E), Section: B.
500 $a Adviser: Arnold W. Miller.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Madison, 2014.
520 $a This thesis contains a few applications of set-theoretic methods to certain problems in real analysis. In the first two sections of Chapter 1, we discuss some results related to a question of Fremlin about partitions of a set of reals into null sets. In Section 3, we answer a questions of Komjath in dimension one. Our proof uses some results of Gitik and Shelah in an essential way. In Chapter 2, we answer a couple of questions about finitely additive total extensions of Lebesgue measure. These problems arose from a question of Juhasz in set-theoretic topology. In Chpater 3, we give some "natural" examples of additive subgroups of reals of arbitrarily high finite Borel rank. The existence of such groups is an old and well known result. In Chapter 4, we construct a non principal ultrafilter from any free maximal ideal in the ring of bounded continuous functions on reals.
590 $a School code: 0262.
650 4 $a Mathematics. $3 515831
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0364
710 2 $a The University of Wisconsin - Madison. $b Mathematics. $3 2101076
773 0 $t Dissertation Abstracts International $g 75-08B(E).
790 $a 0262
791 $a Ph.D.
792 $a 2014
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3620124