×

zbMATH — the first resource for mathematics

Convergence of sequences of real functions with respect to small systems. (English) Zbl 0659.28004
In this paper we define the convergence with respect to small systems and we prove that this convergence and the convergence with respect to a suitable \(\sigma\)-ideal are equivalent in the case of an upper semicontinuous small system. Then we prove that the space \({\mathfrak M}\) of all classes of equivalence of S-measurable real functions is equipped with the Fréchet topology.

MSC:
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
40A30 Convergence and divergence of series and sequences of functions
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] ENGELKING R.: General Topology. Warszawa 1977. · Zbl 0373.54002
[2] NEUBRUNN T., RIEČAN B.: Miera a integrál. Bratislava 1981. · Zbl 0485.28001
[3] RIEČAN B.: Abstract formulation of some theorems of measure theory. Mat.-Fyz. Časopis SAV 16, 1966, 268-273. · Zbl 0174.34402
[4] WAGNER E.: Sequences of measurable functions. Fund. Math. CXII, 1981, 89-102. · Zbl 0386.28005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.