Lusin's Condition \(\mathbf{(N)}\) and Foran's condition \(\mathbf{(M)}\) are Equivalent for Borel Functions that are \(\mathbf{VBG}\) on a Borel Set

Abstract

In this paper we show that Lusin’s condition \((N)\) and Foran’s condition \((M)\) are equivalent for Borel functions that are \(VBG\) on a Borel set. Also new characterizations of conditions \((M)\) and \(\underline{M}\) are given.