Assuming the continuum hypothesis, we obtain a translation invariant version of the following result of E. Grzegorek: There are two countably generated o-algebras on the interval [0, 1 ] such that both carry a nonatomic countably additive probability measure, but the a-algebra generated by their union does not carry any such measure.
- Continuum hypothesis
- Countably generated o-algebra
- Phrases. Translation invariant measure