Handbook of Measure Theory
In two volumesBy
- E. Pap
The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations 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 whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.
Mathematicians (Researchers, Postgraduate, students)Knowledge and Artificial Intelligence EngineersEconomists (Decision Making)
Published: October 2002
A collection of the work of 43 contributors, oustanding specialists, whose names, as well as the editor name, quarantee a high qualityof the content.
...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...
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 indistribution (J. Brooks).
Part 2, Vector measures
8. Vector Integration in Banach Spaces and application toStochastic Integration (N. Dinculeanu).
9. The Riesz Theorem (J. Diestel, J. Swart).
10. Stochastic processes and stochastic integration in Banach spaces (J. Brooks).
Part 3, Integration theory
11. Daniell integral and related topics (M. D. Carillo).
12. Pettis integral (K. Musial).
13. The Henstock-Kurzweil integral (B. Bongiorno).
14. Integration of multivalued functions (Ch. Hess).
Part 4, Topological aspects of measure theory
15. Density topologies (W. Wilczyński).
16. FN-topologies and group-valued measures (H. Weber).
17. On products of topological measure spaces (S. Grekas).
18. Perfect measures and related topics (D. Ramachandran).
Part 5, Order and measure theory
19. Riesz spaces and ideals of measurable functions (M. Väth).
20. Measures on Quantum Structures (A.Dvurečenskij).
21. Probability on MV-algebras (D. Mundici, B. Riečan).
22. Measures on clans and on MV-algebras (G. Barbieri, H. Weber).
23. Triangular norm-based measures (D. Butnariu, E. P. Klement).
Part 6, Geometric measure theory
24. Geometric measure theory: selected concepts, results andproblems (M. Chlebik).
25. Fractal measures (K. J. Falconer).
Part 7, Relation to transformation and duality
26. Positive and complex Radon measures on locally compactHausdorff spaces (T. V. Panchapagesan).
27. Measures on algebraic-topological structures (P. Zakrzewski).
28. Liftings (W. Strauss, N. D. Macheras, K. Musial).
29. Ergodic theory (F. Blume).
30. Generalized derivative (E. Pap, A. Takači).
Part 8, Relation to the foundations of mathematics
31. Real valued measurability, some set theoretic aspects (A.Jovanović).
32. Nonstandard Analysis and Measure Theory (P. Loeb).
Part 9, Non-additive measures
33. Monotone set-functions-based integrals (P. Benvenuti, R.Mesiar, D. Vivona).
34. Set functions over finite sets: transformations and integrals(M. Grabisch).
35. Pseudo-additive measures and their applications (E. Pap).
36. Qualitative possibility functions and integrals (D. Dubois, H.Prade).
37. Information measures (W. Sander).