Displaying similar documents to “Convergence theorems for the PU-integral”

Relativization of some aspects of the theory of functions of bounded variation

Krishna M. Garg

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We present here relativized versions of some aspects of the theory of functions of bounded variation, viz. relative to a function of bounded variation, without going into relative bounded variation. A few results have been known in this direction for some time when the functions involved are continuous, but due to the complications that arise when the functions are discontinuous, no systematic attempt seems to have been made in this direction in the past.Let B denote the linear space...

Convergence theorems for the Birkhoff integral

Marek Balcerzak, Monika Potyrała (2008)

Czechoslovak Mathematical Journal

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We give sufficient conditions for the interchange of the operations of limit and the Birkhoff integral for a sequence ( f n ) of functions from a measure space to a Banach space. In one result the equi-integrability of f n ’s is involved and we assume f n → f almost everywhere. The other result resembles the Lebesgue dominated convergence theorem where the almost uniform convergence of ( f n ) to f is assumed.

A descriptive definition of a BV integral in the real line

Diana Caponetti, Valeria Marraffa (1999)

Mathematica Bohemica

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A descriptive characterization of a Riemann type integral, defined by BV partition of unity, is given and the result is used to prove a version of the controlled convergence theorem.