Displaying similar documents to “Relativization of some aspects of the theory of functions of bounded variation”

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.

Convergence theorems for the PU-integral

Giuseppa Riccobono (2000)

Mathematica Bohemica

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We give a definition of uniform PU-integrability for a sequence of μ -measurable real functions defined on an abstract metric space and prove that it is not equivalent to the uniform μ -integrability.

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.