Handbook of Measure Theory
In two volumes
Published on 31. October 2002
1632 pages
978-0-08-053309-4 (ISBN)
Description
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.
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Content
PrefacePart 1, Classical measure theory1. History of measure theory (Dj. Paunic).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. Volcic, D. Candeloro).7. One-dimensional diffusions and their convergence indistribution (J. Brooks).Part 2, Vector measures8. 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 theory11. 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 theory15. Density topologies (W. Wilczynski).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 theory19. Riesz spaces and ideals of measurable functions (M. Väth).20. Measures on Quantum Structures (A.Dvurecenskij).21. Probability on MV-algebras (D. Mundici, B. Riecan).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 theory24. Geometric measure theory: selected concepts, results andproblems (M. Chlebik).25. Fractal measures (K. J. Falconer).Part 7, Relation to transformation and duality26. 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. Takaci).Part 8, Relation to the foundations of mathematics31. Real valued measurability, some set theoretic aspects (A.Jovanovic).32. Nonstandard Analysis and Measure Theory (P. Loeb).Part 9, Non-additive measures33. 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).
