Abstract Let Ω be a Lebesgue-measurable set in ℝn of finite positive Lebesgue measure. In this note we calculate the lack of equi-measurability of the set Kc(Ω), c > 0,… Click to show full abstract
Abstract Let Ω be a Lebesgue-measurable set in ℝn of finite positive Lebesgue measure. In this note we calculate the lack of equi-measurability of the set Kc(Ω), c > 0, of all Lebesgue-measurable functions f : Ω → ℝ such that 0 ≤ f ≤ c, a.e. on Ω. From our result we repair a gap in the Example 2.3 of the paper [APPELL, J.—DE PASCALE, E.: Su alcuni parametri connessi con la misura di non compattezza di Hausdorff in spazi di funzioni misurabili, Boll. Un. Mat. Ital. B (6) 3 (1984), 497–515].
Keywords:
measurable functions;
measurability certain;
lack equi;
equi measurability;
lebesgue measurable
Journal Title: Mathematica Slovaca
Year Published: 2017
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Journal Title: Mathematica Slovaca
Year Published: 2017
Link to full text (if available)
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recommendations!