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Strong Fubini axioms from measure extension axioms. (English) Zbl 0765.03026
The author presents some connections between various cardinal conditions and the Fubini theorem for not necessarily product measurable sets and functions. The main result (Theorem 3.1) states that ZFC + the so-called product measure extension axiom implies some strengthenings of the strong Fubini axiom in the case of Radon measure spaces. Its proof makes use of some ideas of A. Kamburelis [Isr. J. Math. 72, No. 3, 373-380 (1990; Zbl 0738.03019)]. Also connections with recent results of D. H. Fremlin are established.

MSC:
03E35 Consistency and independence results
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
28A35 Measures and integrals in product spaces
03E05 Other combinatorial set theory
03E65 Other set-theoretic hypotheses and axioms
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
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