Control functions and total boundedness in the space .
On the -finiteness of a variational measure
The -finiteness of a variational measure, generated by a real valued function, is proved whenever it is -finite on all Borel sets that are negligible with respect to a -finite variational measure generated by a continuous function.
A descriptive definition of a BV integral in the real line
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.
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