Cardinal conditions for strong Fubini theorems

Author:
Joseph Shipman

Journal:
Trans. Amer. Math. Soc. **321** (1990), 465-481

MSC:
Primary 03E15; Secondary 03E35, 28A20, 28A35

DOI:
https://doi.org/10.1090/S0002-9947-1990-1025758-0

MathSciNet review:
1025758

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Abstract | References | Similar Articles | Additional Information

Abstract: If are cardinals with the cardinality of a nonmeasurable set, and for is the cardinality of a set of reals which is not the union of measure-0 sets, then for *any* nonnegative function all of the iterated integrals

**[C]**Chris Freiling,*Axioms of symmetry: throwing darts at the real number line*, J. Symbolic Logic**51**(1986), no. 1, 190–200. MR**830085**, https://doi.org/10.2307/2273955**[D]**Fremlin, [1983]*Cichón's diagram*, Séminaire Initiation à l'Analyse**23**(1983/84), no. 5.**1.**D. H. Fremlin,*Measure-additive coverings and measurable selectors*, Dissertationes Math. (Rozprawy Mat.)**260**(1987), 116. MR**928693****[H]**Harvey Friedman,*A consistent Fubini-Tonelli theorem for nonmeasurable functions*, Illinois J. Math.**24**(1980), no. 3, 390–395. MR**573474****[M]**Moti Gitik and Saharon Shelah,*Forcings with ideals and simple forcing notions*, Israel J. Math.**68**(1989), no. 2, 129–160. MR**1035887**, https://doi.org/10.1007/BF02772658**[K]***Philosophy of mathematics: Selected readings*, Edited and with an introduction by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR**0166055****[S]**Stanley P. Gudder,*Probability manifolds*, J. Math. Phys.**25**(1984), no. 8, 2397–2401. MR**751521**, https://doi.org/10.1063/1.526461**[T]**Thomas Jech,*Set theory*, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics. MR**506523****[K]**Kenneth Kunen,*Random and Cohen reals*, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 887–911. MR**776639****[I]**Itamar Pitowsky,*Deterministic model of spin and statistics*, Phys. Rev. D (3)**27**(1983), no. 10, 2316–2326. MR**704118**, https://doi.org/10.1103/PhysRevD.27.2316**[A]**A. N. Shiryayev,*Probability*, Graduate Texts in Mathematics, vol. 95, Springer-Verlag, New York, 1984. Translated from the Russian by R. P. Boas. MR**737192****[R]**Robert M. Solovay,*A model of set-theory in which every set of reals is Lebesgue measurable*, Ann. of Math. (2)**92**(1970), 1–56. MR**0265151**, https://doi.org/10.2307/1970696**2.**Robert M. Solovay,*Real-valued measurable cardinals*, Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428. MR**0290961****[S]**Ulam, [1930]*Zur Masstheorie in der algemeinen Mengenlehre*, Fund. Math.**16**(1930), 140-150.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1990-1025758-0

Keywords:
Fubini theorem(s),
real-valued measurable cardinals,
nonmeasurable sets

Article copyright:
© Copyright 1990
American Mathematical Society