Let $\mu$ be a Probability measure and $f:X\to X$ be a homeomorphism. The measure $\mu$ is called an invariant measure for $f$, if $\mu(f^{-1}(A))=\mu(A)$ for all measurable set $A$. Also $x\in X$ is called a periodic point if there is $n\in\mathbb{N}$ with $f^n(x)=x$. $Per(f)$ is the set of periodic points for $f$
Suppose that $\mu$ be an invariant atom measure.
Is it true that $Supp(\mu)\subseteq Per(f)$?