On the lack of equi-measurability for certain sets of Lebesgue-measurable functions

Year, pages: 2017, 1595 - 1601

Let $Ω$ be a Lebesgue-measurable set in $\mathbb{R}ⁿ$ of finite positive Lebesgue measure. In this note we calculate the lack of equi-measurability of the set $K_c(Ω)$, $c>0$, of all Lebesgue-measurable functions $f : Ω \to \mathbb{R}$ 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.: \textit{Su alcuni parametri connessi con la misura di non compattezza di Hausdorff in spazi di funzioni misurabili}, Boll. Un. Mat. Ital. B (6) \textbf{3} (1984), 497–515].

Tavernise, M., Trombetta, A., Trombetta, G. 2017. On the lack of equi-measurability for certain sets of Lebesgue-measurable functions. In Mathematica Slovaca, vol. 67, no.6, pp. 1595-1601. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0073

Tavernise, M., Trombetta, A., Trombetta, G. (2017). On the lack of equi-measurability for certain sets of Lebesgue-measurable functions. Mathematica Slovaca, 67(6), 1595-1601. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0073