Sesquiregular Measures in Product Spaces and Convolution of Such Measures
We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function defined on a non-degenerate closed subinterval of in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure generated by the primitive of , where is the family of all closed non-degenerate subintervals of .
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.
It is shown that measure extension axioms imply various forms of the Fubini theorem for nonmeasurable sets and functions in Radon measure spaces.