My problem is as follows.
We have a measurable space (X,F) and a set function \mu :F \rightarrow [0,1] satisfying the following conditions:
1. \mu (\emptyset)=0
3. if A \subset B then \mu (A) \leq \mu (B).
I call \mu a pseudometric.
I have some measurable function f:X \rightarrow R...