Uniform integrabblity and the lebesgue theorem on convergence in $L_0$-valued measures

  • V. N. Radchenko

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.
Published
25.06.1996
How to Cite
RadchenkoV. N. “Uniform Integrabblity and the Lebesgue Theorem on Convergence in $L_0$-Valued Measures”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 48, no. 6, June 1996, pp. 857-60, https://umj.imath.kiev.ua/index.php/umj/article/view/5287.
Section
Short communications