Read Anywhere and on Any Device!

Special Offer | $0.00

Join Today And Start a 30-Day Free Trial and Get Exclusive Member Benefits to Access Millions Books for Free!

Create Free Account

Quick and Easy Sign Up!

It takes less then 1 minute to sign up, then you can enjoy Unlimited eBooks.

Sign Up Browse

Read Anywhere and on Any Device!

  • Download on iOS
  • Download on Android
  • Download on iOS

Nonmeasurable Sets and Functions. North-Holland Mathematics Studies, Volume 195.

Alexander Kharazishvili
4.9/5 (20577 ratings)
Read Now Download Now ⏭ listen AudioBook
Description:The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics: 1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces; 2. The theory of non-real-valued-measurable cardinals; 3. The theory of invariant (quasi-invariant) extensions of invariant (quasi-invariant) measures. These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Nonmeasurable Sets and Functions. North-Holland Mathematics Studies, Volume 195.. To get started finding Nonmeasurable Sets and Functions. North-Holland Mathematics Studies, Volume 195., you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.
Pages
349
Format
PDF, EPUB & Kindle Edition
Publisher
Elsevier Science & Technology
Release
2004
ISBN
1281008885

Nonmeasurable Sets and Functions. North-Holland Mathematics Studies, Volume 195.

Alexander Kharazishvili
4.4/5 (1290744 ratings)
Read Now Download now ⏭ listen AudioBook
Description: The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics: 1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces; 2. The theory of non-real-valued-measurable cardinals; 3. The theory of invariant (quasi-invariant) extensions of invariant (quasi-invariant) measures. These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Nonmeasurable Sets and Functions. North-Holland Mathematics Studies, Volume 195.. To get started finding Nonmeasurable Sets and Functions. North-Holland Mathematics Studies, Volume 195., you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.
Pages
349
Format
PDF, EPUB & Kindle Edition
Publisher
Elsevier Science & Technology
Release
2004
ISBN
1281008885

More Books

Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions (Atlantis Studies in Mathematics) by Alexander Kharazishvili (2009-11-10)

Topics in Measure Theory and Real Analysis: The Measure Extension Problem and Related Questions (Atlantis Studies in Mathematics) by Alexander Kharazishvili (2009-11-10)

4.4/5 (1,282,506 ratings)

Set Theoretical Aspects of Real Analysis (Monographs and Research Notes in Mathematics) by Alexander B. Kharazishvili (2014-08-21)

Set Theoretical Aspects of Real Analysis (Monographs and Research Notes in Mathematics) by Alexander B. Kharazishvili (2014-08-21)

4.2/5 (4,466 ratings)

Set Theoretical Aspects of Real Analysis (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Set Theoretical Aspects of Real Analysis (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

4.1/5 (1,751 ratings)

Strange Functions in Real Analysis. Pure and Applied Mathematics

Strange Functions in Real Analysis. Pure and Applied Mathematics

4.5/5 (743 ratings)

TRANSFORMATION GROUPS AND INVARIANT MEASURES: SET-THEORETICAL ASPECTS

TRANSFORMATION GROUPS AND INVARIANT MEASURES: SET-THEORETICAL ASPECTS

4/5 (647 ratings)

Introduction to Combinatorial Methods in Geometry

Introduction to Combinatorial Methods in Geometry

4/5 (647 ratings)

Notes on Real Analysis and Measure Theory: Fine Properties of Real Sets and Functions (Springer Monographs in Mathematics)

Notes on Real Analysis and Measure Theory: Fine Properties of Real Sets and Functions (Springer Monographs in Mathematics)

4.7/5 (647 ratings)

Strange Functions in Real Analysis

Strange Functions in Real Analysis

4.6/5 (647 ratings)

4.9/5 (647 ratings)
loader