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Zaharov, V.

Topological and algebraical aspects of some sets of measurable functions. (English) Zbl 0508.54008

General topology and its relations to modern analysis and algebra V, Proc. 5th Prague Topol. Symp. 1981, Sigma Ser. Pure Math. 3, 706-712 (1983).
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MSC:

54C35 Function spaces in general topology
28C05 Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
46B42 Banach lattices
46F15 Hyperfunctions, analytic functionals
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
54C30 Real-valued functions in general topology
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
06B23 Complete lattices, completions
54G05 Extremally disconnected spaces, \(F\)-spaces, etc.

Keywords:

measurable Borel functions and hyperfunctions; characterization of the hyperstonian absolute of completely regular space; elevation of Borel sets and functions; characterization and functional description of the Lebesgue extension of the vector lattice of bounded continuous functions; module of Borel hyperfunctions; uniform completion; hyperdivisible envelope of the module of Lusin hyperfunctions; Dedekind complete vector lattice extension; perfect extremally disconnected preimage; Radon measures; hyper-Stonian cover

Citations:

Zbl 0374.54026; Zbl 0484.00009
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