國立高雄大學圖資館 |

登入

回首頁

Notes on real analysis and measure theoryfine properties of real sets and functions /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Notes on real analysis and measure theoryby Alexander Kharazishvili.
其他題名:	fine properties of real sets and functions /
作者:	Kharazishvili, A. B.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xi, 253 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Functions of real variables.
電子資源:	https://doi.org/10.1007/978-3-031-17033-1
ISBN:	9783031170331$q(electronic bk.)

Notes on real analysis and measure theoryfine properties of real sets and functions /
Kharazishvili, A. B.

Notes on real analysis and measure theoryfine properties of real sets and functions /[electronic resource] :by Alexander Kharazishvili. - Cham :Springer International Publishing :2022. - xi, 253 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

Preface -- 1. Real-Valued Semicontinuous Functions -- 2. The Oscillations of Real-Valued Functions -- 3. Monotone and Continuous Restrictions of Real-Valued Functions -- 4. Bijective Continuous Images of Absolute Null Sets -- 5. Projective Absolutely Nonmeasurable Functions -- 6. Borel Isomorphisms of Analytic Sets -- 7. Iterated Integrals of Real-Valued Functions of Two Real Variables -- 8. The Steinhaus Property, Ergocidity, and Density Points -- 9. Measurability Properties of H-Selectors and Partial H-Selectors -- 10. A Decomposition of an Uncountable Solvable Group into Three Negligible Sets -- 11. Negligible Sets Versus Absolutely Nonmeasurable Sets -- 12. Measurability Properties of Mazurkiewicz Sets -- 13. Extensions of Invariant Measures on R -- A. A Characterization of Uncountable Sets in Terms of their Self-Mappings -- B. Some Applications of Peano Type Functions -- C. Almost Rigid Mathematical Structures -- D. Some Unsolved Problems in Measure Theory -- Bibliography -- Index.

This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.

ISBN: 9783031170331$q(electronic bk.)

Standard No.: 10.1007/978-3-031-17033-1doiSubjects--Topical Terms:

189525
Functions of real variables.

LC Class. No.: QA331.5 / .K43 2022

Dewey Class. No.: 515.8

Notes on real analysis and measure theoryfine properties of real sets and functions /
LDR:02806nmm a2200337 a 4500 001 630686
003 DE-He213
005 20220923084624.0
006 m d
007 cr nn 008maaau
008 230329s2022 sz s 0 eng d
020 $a 9783031170331$q(electronic bk.)
020 $a 9783031170324$q(paper)
024 7 $a 10.1007/978-3-031-17033-1 $2 doi
035 $a 978-3-031-17033-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA331.5 $b .K43 2022
072 7 $a PB $2 bicssc
072 7 $a MAT000000 $2 bisacsh
072 7 $a PB $2 thema
082 0 4 $a 515.8 $2 23
090 $a QA331.5 $b .K45 2022
100 1 $a Kharazishvili, A. B. $3 198916
245 1 0 $a Notes on real analysis and measure theory $h [electronic resource] : $b fine properties of real sets and functions / $c by Alexander Kharazishvili.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a xi, 253 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a Preface -- 1. Real-Valued Semicontinuous Functions -- 2. The Oscillations of Real-Valued Functions -- 3. Monotone and Continuous Restrictions of Real-Valued Functions -- 4. Bijective Continuous Images of Absolute Null Sets -- 5. Projective Absolutely Nonmeasurable Functions -- 6. Borel Isomorphisms of Analytic Sets -- 7. Iterated Integrals of Real-Valued Functions of Two Real Variables -- 8. The Steinhaus Property, Ergocidity, and Density Points -- 9. Measurability Properties of H-Selectors and Partial H-Selectors -- 10. A Decomposition of an Uncountable Solvable Group into Three Negligible Sets -- 11. Negligible Sets Versus Absolutely Nonmeasurable Sets -- 12. Measurability Properties of Mazurkiewicz Sets -- 13. Extensions of Invariant Measures on R -- A. A Characterization of Uncountable Sets in Terms of their Self-Mappings -- B. Some Applications of Peano Type Functions -- C. Almost Rigid Mathematical Structures -- D. Some Unsolved Problems in Measure Theory -- Bibliography -- Index.
520 $a This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.
650 0 $a Functions of real variables. $3 189525
650 0 $a Measure theory. $3 182047
650 1 4 $a Mathematics. $3 184409
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 557774
856 4 0 $u https://doi.org/10.1007/978-3-031-17033-1
950 $a Mathematics and Statistics (SpringerNature-11649)