Abstract
It is proved that for a wide class of bases in ${\mathbb R}^m$ a function generates a $\sigma$-finite absolutely continuous variational measure if and only if this function belongs to $ACG_\delta$-class. It is also shown that under some additional assumptions on a basis, $\sigma$-finiteness follows from the absolute continuity of the variational measure.
Citation
Valentin Skvortsov. Yurij Zherebyov. "On classes of functions generating absolutely continuous variational measures." Real Anal. Exchange 30 (1) 361 - 372, 2004-2005.
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