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Some remarks on descriptive characterizations of the strong McShane integral

Sokol Bush Kaliaj (2019)

Mathematica Bohemica

We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function f : W X defined on a non-degenerate closed subinterval W of m in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure V F generated by the primitive F : W X of f , where W is the family of all closed non-degenerate subintervals of W .

Some Remarks on Functionals with the Tensorization Property

Paweł Wolff (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We investigate the subadditivity property (also known as the tensorization property) of φ-entropy functionals and their iterations. In particular we show that the only iterated φ-entropies with the tensorization property are iterated variances. This is a complement to the result due to Latała and Oleszkiewicz on characterization of the standard φ-entropies with the tensorization property.

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.

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