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.
Mathematicians (Researchers, Postgraduate, students) Knowledge and Artificial Intelligence Engineers Economists (Decision Making)
Part 1, Classical measure theory
- History of measure theory (Dj. Paunić).
- Some elements of the classical measure theory (E. Pap).
- Paradoxes in measure theory (M. Laczkovich).
- Convergence theorems for set functions (P. de Lucia, E. Pap).
- Differentiation (B. S. Thomson).
- Radon-Nikodým theorems (A. Volčič, D. Candeloro).
- One-dimensional diffusions and their convergence in
distribution (J. Brooks).
Part 2, Vector measures
- Vector Integration in Banach Spaces and application to
Stochastic Integration (N. Dinculeanu).
- The Riesz Theorem (J. Diestel, J. Swart).
- Stochastic processes and
stochastic integration in Banach spaces (J. Brooks).
Part 3, Integration theory
- Daniell integral and related topics (M. D. Carillo).
- Pettis integral (K. Musial).
- The Henstock-Kurzweil integral (B. Bongiorno).
- Integration of multivalued functions (Ch. Hess).
Part 4, Topological aspects of measure theory
- Density topologies (W. Wilczyński).
- FN-topologies and group-valued measures (H. Weber).
- On products of topological measure spaces (S. Grekas).
- Perfect measures and related topics (D. Ramachandran).
Part 5, Order and measure theory
- Riesz spaces and ideals of measurable functions (M. Väth).
- Measures on Quantum Structures (A.
- Probability on MV-algebras (D. Mundici, B. Riečan).
- Measures on clans and on MV-algebras (G. Barbieri, H. Weber).
- Triangular norm-based measures (D. Butnariu, E. P. Klement).
Part 6, Geometric measure theory
- Geometric measure theory: selected concepts, results and
problems (M. Chlebik).
- Fractal measures (K. J. Falconer).
Part 7, Relation to transformation and duality
- Positive and complex Radon measures on locally compact
Hausdorff spaces (T. V. Panchapagesan).
- Measures on algebraic-topological structures (P. Zakrzewski).
- Liftings (W. Strauss, N. D. Macheras, K. Musial).
- Ergodic theory (F. Blume).
- Generalized derivative (E. Pap, A. Takači).
Part 8, Relation to the foundations of mathematics
- Real valued measurability, some set theoretic aspects (A.
- Nonstandard Analysis and Measure Theory (P. Loeb).
Part 9, Non-additive measures
Monotone set-functions-based integrals (P. Benvenuti, R. Mesiar, D. Vivona).
Set functions over finite sets: transformations and integrals (M. Grabisch).
Pseudo-additive measures and their applications (E. Pap).
Qualitative possibility functions and integrals (D. Dubois, H. Prade).
- Information measures (W. Sander).
- No. of pages:
- © North Holland 2002
- 31st October 2002
- North Holland
- eBook ISBN:
- Hardcover ISBN:
University of Novi Sad, Institute of Mathematics, Yugoslavia
@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