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Ukrainian Mathematical Journal

, Volume 48, Issue 6, pp 965–969 | Cite as

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

  • V. N. Radchenko
Brief Communications

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.

Keywords

Measurable Function Real Function Simple Function Vector Measure Convergent Subsequence 
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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. N. Radchenko

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