A further investigation for fuzzy measures on metric spaces
A set function \(m: B\to [0,\infty]\) defined on the family of all Borel subsets of a metric space is an LSC-fuzzy measure if \(m(\emptyset)=0\), \(m\) is monotone and continuous from below. It is said to be exhaustive if \(\lim m(E_n)= 0\) for any disjoint sequence \((E_n)\). It is said to have the pseudometric generating property if, for any \(\varepsilon> 0\), there exists \(\delta>0\) such that \(m(E\cup F)< \varepsilon\) whenever \(m(E)< \delta\) and \(m(F)<\delta\). In the paper the Egorov and Luzin theorems are proved in the case that there is given an LSC-fuzzy measure that is exhaustive and has the pseudometric generating property.
scientific article; zbMATH DE number 1339628