Let $(Y, B(Y))$ be a measurable space where Y is a metric space and B(Y) the Borel Sigma algebra generated by the standard topology on Y.
Let $f: (X, B(X)) \to (Y, B(Y)) $ and let $$ v: B(Y) \to [0, + \infty]$$ $$ A \to m(f^{-1}(A))$$
(where X is a separable metric space and $m$ a measure on the measurable space $(X, B(X))$.
My question is simple: What is the support of $v$?