Abstract:
We define the gamma-compactification of an arbitrary measurable space and study its structure and properties in the general and topological cases. We introduce and study the notion of gamma-extension of a singleton in a topological space. We consider the procedure of extension of finitely additive measures from the original space to regular countably additive measures on the gamma-compactification of the space.
Keywords:compactification of measurable space, compactification of topological space, one-point compactification, finitely additive measure, purely finitely additive measure, countably additive measure, extension of measure.
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