Probability measure over bijection map Let $P$ a probability measure over $\mathbb{R}^n$. Let $f: A \rightarrow B$ a bijection from $A$ to $B$ two sets of $\mathbb{R}^n$. Does the following equality could be hold?
$$
P(f(A)) = P(A).
$$
Thanks, 
S

No. We have $f(A)=B$, and since $B$ can have a different measure than $A$ the equality does not hold always.
