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

• Date: 1996
• Main Authors: Radchenko, V. N., Радченко, В. Н.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 1996
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5287
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 $L_0$-value...