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- W4236914292 abstract "If ${kappa _1},{kappa _2}, ldots ,{kappa _n}$ are cardinals with ${kappa _1}$ the cardinality of a nonmeasurable set, and for $i = 2,3, ldots ,n$ ${kappa _i}$ is the cardinality of a set of reals which is not the union of ${kappa _{i - 1}}$ measure-$0$ sets, then for any nonnegative function $f:{{mathbf {R}}^n} to {mathbf {R}}$ all of the iterated integrals [ {I_sigma } = iint cdots int {f({x_1},{x_2}, ldots ,{x_n})d{x_{sigma (1)}}d{x_{sigma (2)}} cdots d{x_{sigma (n)}},quad sigma in {S_n}} ], which exist are equal. If all $n!$ of the integrals exist, then the weaker condition of the case $n = 2$ implies they are equal. These cardinal conditions are consistent with and independent of ZFC, and follow from the existence of a real-valued measure on the continuum. Other necessary conditions and sufficient conditions for the existence and equality of iterated integrals are also treated." @default.
- W4236914292 created "2022-05-12" @default.
- W4236914292 creator A5030127015 @default.
- W4236914292 date "1990-10-01" @default.
- W4236914292 modified "2023-09-26" @default.
- W4236914292 title "Cardinal Conditions for Strong Fubini Theorems" @default.
- W4236914292 doi "https://doi.org/10.2307/2001569" @default.
- W4236914292 hasPublicationYear "1990" @default.
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