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On the $σ$ -finiteness of a variational measure

Diana Caponetti — 2003

Mathematica Bohemica

The $σ$ -finiteness of a variational measure, generated by a real valued function, is proved whenever it is $σ$ -finite on all Borel sets that are negligible with respect to a $σ$ -finite variational measure generated by a continuous function.

A descriptive definition of a BV integral in the real line

Diana Caponetti; Valeria Marraffa — 1999

Mathematica Bohemica

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.

Control functions and total boundedness in the space $L_{0}$ .

Caponetti, Diana; Lewicki, Grzegorz; Trombetta, Giulio — 2002

Novi Sad Journal of Mathematics

Page 1

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