On abstract Fubini theorems for finitely additive integration
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- by E. de Amo and M. Díaz Carrillo
- Proc. Amer. Math. Soc. 123 (1995), 2739-2744
- DOI: https://doi.org/10.1090/S0002-9939-1995-1257101-6
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Abstract:
A Fubini theorem for positive linear functionals on the vector lattice of the real-valued functions is given. This result properly contains that of the Riemann-$\mu$-abstract integral.References
- Aumann Georg, Integralerweiterungen mittels Normen, Arch. Math. (Basel) 3 (1952), 441–450 (German). MR 54693, DOI 10.1007/BF01900560
- P. Bobillo Guerrero and M. Díaz Carrillo, Summable and integrable functions with respect to any Loomis system, Arch. Math. (Basel) 49 (1987), no. 3, 245–256. MR 906739, DOI 10.1007/BF01271664
- Manuel Díaz Carrillo and Pilar Muñoz Rivas, Finitely additive integration: integral extension with local convergence, Ann. Sci. Math. Québec 17 (1993), no. 2, 145–154. MR 1259371 N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1957.
- Jürgen Elsner, Zum “Satz von Fubini” für ein abstraktes Riemann Integral, Math. Z. 141 (1975), 265–278 (German). MR 360987, DOI 10.1007/BF01247312
- Klaus Floret, Maß- und Integrationstheorie, Teubner Studienbücher Mathematik. [Teubner Mathematical Textbooks], B. G. Teubner, Stuttgart, 1981 (German). Eine Einführung. [An introduction]. MR 609518, DOI 10.1007/978-3-322-93106-1
- G. G. Gould, The Daniell-Bourbaki Integral for finitely additive measures, Proc. London Math. Soc. (3) 16 (1966), 297–320. MR 204606, DOI 10.1112/plms/s3-16.1.297
- Hans Günzler, Linear functionals which are integrals, Rend. Sem. Mat. Fis. Milano 43 (1973), 167–176 (1974) (English, with Italian summary). MR 354987, DOI 10.1007/BF02924845
- Hans Günzler, Integration, Bibliographisches Institut, Mannheim, 1985 (German). MR 802205
- H. Günzler, Convergence theorems for a Daniell-Loomis integral, Math. Pannon. 2 (1991), no. 2, 77–94. MR 1149951
- Dieter Hoffmann, Zum “Satz von Fubini”, J. Reine Angew. Math. 292 (1977), 138–145. MR 437707, DOI 10.1515/crll.1977.292.138
- L. H. Loomis, Linear functionals and content, Amer. J. Math. 76 (1954), 168–182. MR 60145, DOI 10.2307/2372407
- Washek F. Pfeffer, Integrals and measures, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 42, Marcel Dekker, Inc., New York-Basel, 1977. MR 0460580
- F. W. Schäfke, Lokale Integralnormen und verallgemeinerte uneigentliche Riemann-Stieltjes-Integrale, J. Reine Angew. Math. 289 (1977), 118–134 (German). MR 453968, DOI 10.1515/crll.1977.289.118
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2739-2744
- MSC: Primary 28A35; Secondary 28C05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1257101-6
- MathSciNet review: 1257101