Handbook of Measure Theory - 1st Edition - ISBN: 9780444502636, 9780080533094

Handbook of Measure Theory

1st Edition

In two volumes

Authors: E. Pap
eBook ISBN: 9780080533094
Hardcover ISBN: 9780444502636
Imprint: North Holland
Published Date: 31st October 2002
Page Count: 1632
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Description

The main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the various areas they contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. The reader may find in the Handbook many close relations to other mathematical areas: real analysis, probability theory, statistics, ergodic theory, functional analysis, potential theory, topology, set theory, geometry, differential equations, optimization, variational analysis, decision making and others. The Handbook is a rich source of relevant references to articles, books and lecture notes and it contains for the reader's convenience an extensive subject and author index.

Readership

Mathematicians (Researchers, Postgraduate, students) Knowledge and Artificial Intelligence Engineers Economists (Decision Making)

Table of Contents

Preface

Part 1, Classical measure theory

  1. History of measure theory (Dj. Paunić).
  2. Some elements of the classical measure theory (E. Pap).
  3. Paradoxes in measure theory (M. Laczkovich).
  4. Convergence theorems for set functions (P. de Lucia, E. Pap).
  5. Differentiation (B. S. Thomson).
  6. Radon-Nikodým theorems (A. Volčič, D. Candeloro).
  7. One-dimensional diffusions and their convergence in distribution (J. Brooks).

Part 2, Vector measures

  1. Vector Integration in Banach Spaces and application to Stochastic Integration (N. Dinculeanu).
  2. The Riesz Theorem (J. Diestel, J. Swart).
  3. Stochastic processes and stochastic integration in Banach spaces (J. Brooks).
    Part 3, Integration theory
  4. Daniell integral and related topics (M. D. Carillo).
  5. Pettis integral (K. Musial).
  6. The Henstock-Kurzweil integral (B. Bongiorno).
  7. Integration of multivalued functions (Ch. Hess).

Part 4, Topological aspects of measure theory

  1. Density topologies (W. Wilczyński).
  2. FN-topologies and group-valued measures (H. Weber).
  3. On products of topological measure spaces (S. Grekas).
  4. Perfect measures and related topics (D. Ramachandran).

Part 5, Order and measure theory

  1. Riesz spaces and ideals of measurable functions (M. Väth).
  2. Measures on Quantum Structures (A. Dvurečenskij).
  3. Probability on MV-algebras (D. Mundici, B. Riečan).
  4. Measures on clans and on MV-algebras (G. Barbieri, H. Weber).
  5. Triangular norm-based measures (D. Butnariu, E. P. Klement).

Part 6, Geometric measure theory

  1. Geometric measure theory: selected concepts, results and problems (M. Chlebik).
  2. Fractal measures (K. J. Falconer).

Part 7, Relation to transformation and duality

  1. Positive and complex Radon measures on locally compact Hausdorff spaces (T. V. Panchapagesan).
  2. Measures on algebraic-topological structures (P. Zakrzewski).
  3. Liftings (W. Strauss, N. D. Macheras, K. Musial).
  4. Ergodic theory (F. Blume).
  5. Generalized derivative (E. Pap, A. Takači).

Part 8, Relation to the foundations of mathematics

  1. Real valued measurability, some set theoretic aspects (A. Jovanović).
  2. Nonstandard Analysis and Measure Theory (P. Loeb).

Part 9, Non-additive measures

  1. Monotone set-functions-based integrals (P. Benvenuti, R. Mesiar, D. Vivona).

  2. Set functions over finite sets: transformations and integrals (M. Grabisch).

  3. Pseudo-additive measures and their applications (E. Pap).

  4. Qualitative possibility functions and integrals (D. Dubois, H. Prade).

    1. Information measures (W. Sander).

Details

No. of pages:
1632
Language:
English
Copyright:
© North Holland 2002
Published:
Imprint:
North Holland
eBook ISBN:
9780080533094
Hardcover ISBN:
9780444502636

About the Author

E. Pap

Affiliations and Expertise

University of Novi Sad, Institute of Mathematics, Yugoslavia

Reviews

@qu:A collection of the work of 43 contributors, oustanding specialists, whose names, as well as the editor name, quarantee a high qualityof the content. @source:Mathematica Slovaca @qu:...chapters contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. ... The handbook is a rich source of relevant references to articles, books and lecture notes... @source:L'Enseignement