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Theorem on the minorant. The denumerability of Maharam's problem

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Abstract

It is proved that on a normed denumerably complete Boolean algebra each continuous exterior measure majorizes at least one measure. With the aid of this result and of the Kelley numbers, Maharam's well-known problem on the seminormability and normability of Boolean algebras is transformed to a problem on the additive minorants of semimeasures continuous from one side on denumerable algebras.

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Authors and Affiliations

  1. Komi State Pedagogic Institute, USSR

    V. N. Aleksyuk

Authors
  1. V. N. Aleksyuk
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Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 597–604, May, 1977.

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Aleksyuk, V.N. Theorem on the minorant. The denumerability of Maharam's problem. Mathematical Notes of the Academy of Sciences of the USSR 21, 336–340 (1977). https://doi.org/10.1007/BF01788228

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  • DOI: https://doi.org/10.1007/BF01788228

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