Displaying similar documents to “A full descriptive definition of the BV-integral”

A concept of absolute continuity and a Riemann type integral

B. Bongiorno, Washek Frank Pfeffer (1992)

Commentationes Mathematicae Universitatis Carolinae

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We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation.

A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities

Dirk Jens F. Nonnenmacher (1994)

Annales Polonici Mathematici

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Modifying Mawhin's definition of the GP-integral we define a well-behaved integral over n-dimensional compact intervals. While its starting definition is of Riemann type, we also establish an equivalent descriptive definition involving characteristic null conditions. This characterization is then used to obtain a quite general form of the divergence theorem.

How subadditive are subadditive capacities?

George L. O'Brien, Wim Vervaat (1994)

Commentationes Mathematicae Universitatis Carolinae

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Subadditivity of capacities is defined initially on the compact sets and need not extend to all sets. This paper explores to what extent subadditivity holds. It presents some incidental results that are valid for all subadditive capacities. The main result states that for all hull-additive capacities (a class that contains the strongly subadditive capacities) there is countable subadditivity on a class at least as large as the universally measurable sets (so larger than the analytic...