Abstract
It is well known that the following theorem due to Banach and Zarecki: $AC = VB ⋂ (N) ⋂ \mathcal{C}$, on a closed set. In [1] we showed that this theorem is no longer true if $AC$ and $VB$ are replaced by Foran's conditions $A(2)$ and $B(2)$, respectively. In the present paper, we introduce the classes $AC_∞$ and $VB_∞$, which contain strictly the classes $AC$ and $VB$, respectively. Then we show that $AC_∞ = VB_∞ ⋂ (N)$, for bounded measurable functions on a measurable set.
Citation
Vasile Ene. "A GENERALIZATION OF THE BANACH ZARECKI THEOREM." Real Anal. Exchange 20 (2) 639 - 646, 1994/1995. https://doi.org/10.2307/44152546
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