Original Articles

Absolute continuity of vector measures and operators

Published in: Quaestiones Mathematicae
Volume 28 , issue 4 , 2005 , pages: 479–485

DOI: 10.2989/16073600509486142

Author(s): Changsun Choi , M. de Kock

Keywords: VECTOR MEASURE , ABSOLUTE CONTINUITY , RYBAKOV CONTROL MEASURE

Abstract

In this paper we show that, for two regular Borel probabilities μ and ν on a compact Hausdorff space Ω, absolute continuity of measures μ &Lt ν is equivalent to absolute continuity of inclusion operators [C(Ω) ↪ L ¹(μ)] ≪ [C(Ω) ↪ L ¹(ν)]. We then generalize this to vector valued cases.

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