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Let $(X,\mu)$ be a probability measure space and $A$ be a measurable subset of $X$ such that $0 \le \mu(A) < p < 1$.
When is it true that there exists a measurable $B \subseteq X$ such that $A \subset B$$A \subseteq B$ and $\mu(B)=p$ ?
When is it true that there exists a measurable $B \subseteq X$ such that $A \subset B$ and $\mu(B)=p$ ?
When is it true that there exists a measurable $B \subseteq X$ such that $A \subseteq B$ and $\mu(B)=p$ ?
