Fubini theorems for Orlicz spaces of Lebesgue-Bochner measurable functions

Author:
Vernon Zander

Journal:
Proc. Amer. Math. Soc. **32** (1972), 102-110

MSC:
Primary 46E30; Secondary 28A35

DOI:
https://doi.org/10.1090/S0002-9939-1972-0291791-4

MathSciNet review:
0291791

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Abstract: Let be the volume space formed as the product of the volume spaces . Let be a pair of complementary (continuous) Young's functions, let , be Banach spaces, let *w* be a multilinear continuous operator on . Let be the Orlicz space of Lebesgue-Bochner measurable functions generated by *p*, and let be the associated space of finitely additive *Z*-valued set functions. The principal result of this paper is as follows: Let . Then (a) the function is -Orlicz summable -a.e.; (b) the operator defined by the expression -a.e. is bilinear and continuous from into , where , where is the Banach space of bounded linear operators from into *W*, and where *N* is the set of -valued -measurable functions of zero seminorm; (c) the equality holds for all , where for all .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0291791-4

Keywords:
Fubini theorem,
Orlicz spaces,
finitely additive set functions,
Lebesgue-Bochner measurable functions

Article copyright:
© Copyright 1972
American Mathematical Society