extension of a non-finite measure For a finite measure on a field $\mathcal{F_0}$ there always exists its extension to $\sigma(\mathcal{F_0})$. 
Can somebody give me an example of a non-finite measure on a field which cannot be extended to $\sigma(\mathcal{F_0})$.
It would be better if somebody can point in the proof (for existence of extension of finite measure), where the finite-ness property is used.

Since Carathéodory's extension theorem does not require that the spaces are sigma-finite, there is no such counterexample. (As already mentioned, in the absence of sigma-finiteness, the uniqueness disappears, not the existence.)
