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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1968, Volume 3, Issue 1, Pages 71–76 (Mi mz6653)

The complementation of an additive measure up to $\sigma$-additivity by means of an extension of the space

D. N. Dudin

M. V. Lomonosov Moscow State University

Abstract: For an algebra $\mathfrak A$ of subsets of a set X there is constructed a set $\widetilde X\supset X$ and an algebra of its subsets so that the mapping $\widetilde A\to A=\mathop\mathfrak A\limits^\sim\cap A$ is a one-to-one correspondence between $\mathop\mathfrak A\limits^\sim$ and $\mathfrak A$ and for each additive measure $M$ on $\mathfrak A$ the measure $\widetilde\mu$ on $\mathop\mathfrak A\limits^\sim$ defined by the equation $\widetilde\mu(\widetilde A)=\mu(A)$ is countably additive.

Full text: PDF file (409 kB)

English version:
Mathematical Notes, 1968, 3:1, 42–44

Bibliographic databases:

UDC: 517.5

Citation: D. N. Dudin, “The complementation of an additive measure up to $\sigma$-additivity by means of an extension of the space”, Mat. Zametki, 3:1 (1968), 71–76; Math. Notes, 3:1 (1968), 42–44

Citation in format AMSBIB
\Bibitem{Dud68} \by D.~N.~Dudin \paper The complementation of an~additive measure up to $\sigma$-additivity by means of an~extension of the space \jour Mat. Zametki \yr 1968 \vol 3 \issue 1 \pages 71--76 \mathnet{http://mi.mathnet.ru/mz6653} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=222236} \zmath{https://zbmath.org/?q=an:0164.35703} \transl \jour Math. Notes \yr 1968 \vol 3 \issue 1 \pages 42--44 \crossref{https://doi.org/10.1007/BF01386964}