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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.)
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##### 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 · eudml:29765 [4] WAGNER E.: Sequences of measurable functions. Fund. Math. CXII, 1981, 89-102. · Zbl 0386.28005 · eudml:211267
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