Infinite combinatorics in function spaces: category methods. (English) Zbl 1265.26004

The authors investigate the foundational questions in the theory of regular variation, like the search for a minimal common generalization of measurability and the Baire property to serve as a necessary and sufficient condition in the uniform convergence theorem, or to define regular variation in the setting of function spaces over normed groups. The main result is the category embedding theorem, which contains the Kestelman-Borwein-Ditor theorem as a special case, [H. Kestelman, J. London Math. Soc. 22, 130–136 (1947; Zbl 0038.03304)] and [D. Borwein and S. Z. Ditor, Canad. Math. Bull. 21, 497–498 (1978; Zbl 0404.28001)].


26A03 Foundations: limits and generalizations, elementary topology of the line
26A12 Rate of growth of functions, orders of infinity, slowly varying functions
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
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