Uniform integrabblity and the lebesgue theorem on convergence in L 0-valued measures
- 16 Downloads
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.
KeywordsMeasurable Function Real Function Simple Function Vector Measure Convergent Subsequence
Unable to display preview. Download preview PDF.
- 1.L. Drewnowski, “Topological rings of sets, continuous set functions, integration. II,” Bull. Acad. Pol. Sci. Sir. Sci. Math., Astron., Phys., 20, No. 4, 277–286 (1972).Google Scholar
- 2.H. Federer, Geometric Theory of Measure [Russian translation], Nauka, Moscow 1987.Google Scholar
- 3.V. N. Radchenko, “On integrals over random measures a-additive with probability one,” Visn. Kyiv. Univ. Mat. Mekh., Issue 31, 111–114 (1989).Google Scholar
- 4.P. Turpin, “Convexites dans les espaces vectoriels topologiques generaux,” Diss. Math., 131 (1976).Google Scholar