Vitalijeva nemerljiva množica - Zmazek, Gal (Matrika, 2024)
This article delves into the Lebesgue measure’s application to define measures for subsets of real numbers, addressing the introduction of Vitali’s non-measurable set, which creates a contradiction under traditional measurement theories if assumed measurable. It thoroughly examines measurable and non-measurable sets, ?$σ$?-algebras, and the differentiation between Borel and Lebesgue measurable sets. The emphasis is on the identification of non-Borel measurable sets, advancing the understanding of measurement theory in mathematical spaces.
Keywords: Lebesgue measure; Lebesgueova mera; measurable sets; merljive množice; Vitali non-measurable set; Vitalijeva nemerljiva množica