# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

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

### Tom 183 / 2004

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

#### Streszczenie

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.

#### Autorzy

• Stevo TodorcevicUniversité Paris VII, C.N.R.S.
UMR 7056
2 Place Jussieu
75251 Paris, France
and
Department of Mathematics
University of Toronto