Suppose μ and ν are
(nonnegative, countably additive) measures on the same sigma-ring. We say that ν is
quasi-dominant with respect to μ if each measurable set contains a subset with the
same ν-measure, where μ is absolutely continuous with respect to ν on that subset.
In particular, ν is quasi-dominant with respect to μ if μ is sigma-finite. We say that ν
is strongly recessive with respect to μ if the zero measure is the only measure that is
quasi-dominant with respect to μ and less than or equal to ν. Properties of these
relationships are investigated, and applications are given to purely atomic
measures, to the Radon-Nikodým theorem and to a decomposition of product
measures.
