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

Bingham, N. H.; Ostaszewski, A. J.

Publ. Inst. Math., Nouv. Sér. 86(100), 55-73 (2009).

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)].

Reviewer: Slobodanka Janković (Beograd)

MSC:

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

Keywords:

automatic continuity; measurable function; Baire property; generic property; function spaces; additive function; subadditive function; mid-point convex function; regularly varying function

Citations:

Zbl 0038.03304; Zbl 0404.28001