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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.

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

Bibliographic databases:

UDC: 517.5
Received: 14.06.1967

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}


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