A decomposition theorem
Copyright policy )A decomposition theorem
This result remains true in some measure spaces, which have a base, whose cardinal has measure zero [5, p. 64]. By means of the abstract Baire category theory, which was developed in [2-4], we present in this note a new, quite different generalization of Theorem 1. To prove our result we suppose that the reader is familiar with the concept of $3and C-families, introduced in [3 and 2], respectively. In the sequel let X be a topological group, which is a complete, separable, metric space without isolated points.
Analysis on general topological groups, Baire category, Baire spaces, sets of Lebesgue measure zero, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, sets of first category, Baire category from an abstract viewpoint
Analysis on general topological groups, Baire category, Baire spaces, sets of Lebesgue measure zero, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, sets of first category, Baire category from an abstract viewpoint
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