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Some remarks on Gleason measures

P. De Nápoli, M. C. Mariani (2007)

Studia Mathematica

This work is devoted to generalizing the Lebesgue decomposition and the Radon-Nikodym theorem to Gleason measures. For that purpose we introduce a notion of integral for operators with respect to a Gleason measure. Finally, we give an example showing that the Gleason theorem does not hold in non-separable Hilbert spaces.

Strong Fubini axioms from measure extension axioms

Piotr Zakrzewski (1992)

Commentationes Mathematicae Universitatis Carolinae

It is shown that measure extension axioms imply various forms of the Fubini theorem for nonmeasurable sets and functions in Radon measure spaces.

The (sub/super)additivity assertion of Choquet

Heinz König (2003)

Studia Mathematica

The assertion in question comes from the short final section in Theory of capacities of Choquet (1953/54), in connection with his prototype of the subsequent Choquet integral. The problem was whether and when this operation is additive. Choquet had the much more abstract idea that all functionals in a certain wide class must be subadditive, and similarly for superadditivity. His treatment of this point was more like an outline, and his proof limited to a rather narrow special case. Thus the proper...

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