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Let () be the -ring of all (bounded) real-measurable functions on a -measurable space , let be the family of all such that is compact, and let be all that is compact for any . We introduce realcompact subrings of , we show that is a realcompact subring of , and also is a realcompact if and only if is a compact measurable space. For every nonzero real Riesz map , we prove that there is an element such that for every if is a compact measurable space. We confirm...
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