Cardinal conditions for strong Fubini theorems
Author:
Joseph Shipman
Journal:
Trans. Amer. Math. Soc. 321 (1990), 465481
MSC:
Primary 03E15; Secondary 03E35, 28A20, 28A35
MathSciNet review:
1025758
Fulltext PDF Free Access
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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 measure0 sets, then for any nonnegative function all of the iterated integrals , which exist are equal. If all of the integrals exist, then the weaker condition of the case implies they are equal. These cardinal conditions are consistent with and independent of ZFC, and follow from the existence of a realvalued measure on the continuum. Other necessary conditions and sufficient conditions for the existence and equality of iterated integrals are also treated.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199010257580
PII:
S 00029947(1990)10257580
Keywords:
Fubini theorem(s),
realvalued measurable cardinals,
nonmeasurable sets
Article copyright:
© Copyright 1990 American Mathematical Society
