A problem of von Neumann and Maharam about algebras supporting continuous submeasures

Volume 183 / 2004

Stevo Todorcevic Fundamenta Mathematicae 183 (2004), 169-183 MSC: Primary 28A60. DOI: 10.4064/fm183-2-7


We show that a $\sigma $-algebra ${{\mathbb B}}$ carries a strictly positive continuous submeasure if and only if ${{\mathbb B}}$ is weakly distributive and it satisfies the $\sigma $-finite chain condition of Horn and Tarski.


  • Stevo TodorcevicUniversité Paris VII, C.N.R.S.
    UMR 7056
    2 Place Jussieu
    75251 Paris, France
    Department of Mathematics
    University of Toronto
    Toronto, Canada, M5S 3G3
    Centre de Recerca Matèmatica
    Apartat 50
    E-08193 Bellaterra, Spain

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