Handbook of Measure Theory
In two volumes
- E. Pap, University of Novi Sad, Institute of Mathematics, Yugoslavia
Mathematicians (Researchers, Postgraduate, students)Knowledge and Artificial Intelligence EngineersEconomists (Decision Making)
- Published: October 2002
- Imprint: NORTH-HOLLAND
- ISBN: 978-0-444-50263-6
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...
Table of ContentsPreface
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).