This article is cited in 4 papers

On the Denjoy–Luzin Definitions of the Function Classes $ACG$, $ACG^*$, $V\!BG$, and $V\!BG^*$

Yu. A. Zhereb'ev

M. V. Lomonosov Moscow State University

Abstract: An equivalent form of the Denjoy–Luzin definitions of the function classes $ACG$, $ACG^*$, $V\!BG$, and $V\!BG^*$ is suggested. Conditions sufficient for the variational measure and approximation variational measure to be semimoderated are obtained.

Keywords: $ACG$-function, $ACG^*$-function, $V\!BG$-function, $V\!BG^*$-function, $AC$-function, $AC^*$-function, $V\!B$-function, $V\!B^*$-function, variational measure, semimoderated measure.

UDC: 517.518.12

Received: 19.01.2006
Revised: 29.05.2006

DOI: 10.4213/mzm3548

 English version: Mathematical Notes, 2007, 81:1, 183–192

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