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HANDBOOK OF MEASURE THEORY 2 VOLUME SET
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.
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 8. Vector Integration in Banach Spaces and application to Stochastic 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 and problems (M. Chlebik). 25. Fractal measures (K. J. Falconer). Part 7, Relation to transformation and duality 26. Positive and complex Radon measures on locally compact Hausdorff 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).