Uniform integrabblity and the lebesgue theorem on convergence in L 0-valued measures

Abstract

We study integrals ∫fdμ of real functions over L 0-valued measures. We give a definition of convergence of real functions in quasimeasure and, as a special case, in L 0-measure. For these types of convergence, we establish conditions of convergence in probability for integrals over L 0-valued measures, which are analogous to the conditions of uniform integrability and to the Lebesgue theorem.