FOM: Strong Fubini Theorems: reply to Podnieks

[Joe Shipman]

Yes, I knew about Freiling's "Axioms of Symmetry".  His 1986 JSL paper
inspired my thesis (see TAMS 10/90), in which I proposed a variety of
"Strong Fubini Theorems" (statements about existence and equality of
iterated integrals of not-necessarily-measurable functions), gave
necessary conditions and sufficient conditions for them, showed their
consistency and independence, and derived them from RVM.  Freiling's
"symmetry argument" is quite interesting and persuasive, though in my
opinion one can go further and argue for the stronger axiom RVM on
similar grounds (Freiling's application of intuitive notions of
probability and conditional probability when selecting points from an
arbitrary subset of [0,1]^2 seems to presuppose the possibility of a
real-valued measure on all subsets).