Handbook of measure theory. Vol. I and II. (English) Zbl 0998.28001

Amsterdam: North-Holland. xi, 786 p./v.I; xi, 787-1607/v.II (2002).

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The articles of this volume will be reviewed individually.
Publisher’s description: 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 as 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.
Indexed articles:
Paunić, Djura, History of measure theory, 1-26 [Zbl 1019.28001]
Pap, Endre, Some elements of the classical measure theory., 27-82 [Zbl 1042.28001]
Laczkovich, Miklós, Paradoxes in measure theory, 83-123 [Zbl 1027.28001]
de Lucia, Paolo; Pap, Endre, Convergence theorems for set functions., 125-178 [Zbl 1034.28002]
Thomson, Brian S., Differentiation, 179-247 [Zbl 1028.28001]
Candeloro, Domenico; Volčič, Aljoša, Radon-Nikodým theorems., 249-294 [Zbl 1039.28003]
Brooks, James K., One-dimensional diffusions and their convergence in distribution, 295-343 [Zbl 1022.60080]
Dinculeanu, Nicolae, Vector integration in Banach spaces and application to stochastic integration, 345-399 [Zbl 1021.28009]
Diestel, Joe; Swart, Johan, The Riesz theorem, 401-447 [Zbl 1028.46024]
Brooks, James K., Stochastic processes and stochastic integration in Banach spaces, 449-502 [Zbl 1018.60056]
Díaz Carrillo, M., Daniell integral and related topics., 503-530 [Zbl 1096.28008]
Musiał, Kazimierz, Pettis integral., 531-586 [Zbl 1043.28010]
Bongiorno, Benedetto, The Henstock-Kurzweil integral, 587-615 [Zbl 1024.26004]
Hess, Christian, Set-valued integration and set-valued probability theory: An overview, 617-673 [Zbl 1022.60011]
Wilczyński, Władysław, Density topologies, 675-702 [Zbl 1021.28002]
Weber, Hans, FN-topologies and group-valued measures., 703-743 [Zbl 1081.28010]
Grekas, Stratos, On products of topological measure spaces, 745-764 [Zbl 1025.28006]
Ramachandran, Doraiswamy, Perfect measures and related topics, 765-786 [Zbl 1032.28003]
Väth, Martin, Riesz spaces and ideals of measurable functions, 787-825 [Zbl 1018.28003]
Dvurečenskij, Anatolij, Measures on quantum structures, 827-868 [Zbl 1031.28003]
Riečan, Beloslav; Mundici, Daniele, Probability on MV-algebras, 869-909 [Zbl 1017.28002]
Barbieri, Giuseppina; Weber, Hans, Measures on clans and on MV-algebras, 911-945 [Zbl 1019.28009]
Butnariu, Dan; Klement, Erich Peter, Triangular norm-based measures., 947-1010 [Zbl 1035.28015]
Chlebík, Miroslav, Geometric measure theory: Selected concepts, results and problems., 1011-1036 [Zbl 1036.28003]
Falconer, Kenneth J., Fractal measures., 1037-1054 [Zbl 1036.28004]
Panchapagesan, T. V., Positive and complex Radon measures in locally compact Hausdorff spaces., 1055-1090 [Zbl 1043.28012]
Zakrzewski, Piotr, Measures on algebraic-topological structures., 1091-1130 [Zbl 1040.28016]
Strauss, Werner; Macheras, Nikolaos D.; Musiał, Kazimierz, Liftings, 1131-1184 [Zbl 1028.28002]
Blume, Frank, Ergodic theory., 1185-1235 [Zbl 1127.37002]
Pap, Endre; Takači, Arpad, Generalized derivatives, 1237-1260 [Zbl 1023.46043]
Jovanović, Aleksandar, Real valued measurability, some set-theoretic aspects, 1261-1293 [Zbl 1024.03051]
Loeb, Peter A., Nonstandard analysis and measure theory, 1295-1328 [Zbl 1018.28008]
Benvenuti, Pietro; Mesiar, Radko; Vivona, Doretta, Monotone set functions-based integrals., 1329-1379 [Zbl 1099.28007]
Grabisch, Michel, Set functions over finite sets: Transformations and integrals, 1381-1401 [Zbl 1021.28013]
Pap, Endre, Pseudo-additive measures and their applications, 1403-1468 [Zbl 1018.28010]
Dubois, Didier; Prade, Henri, Qualitative possibility functions and integrals, 1469-1522 [Zbl 1018.28009]
Sander, Wolfgang, Measures of information, 1523-1565 [Zbl 1031.94005]


28-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to measure and integration
28-06 Proceedings, conferences, collections, etc. pertaining to measure and integration
00B15 Collections of articles of miscellaneous specific interest