Can you provide me a counter example for this.

Suppose that I have a sequence of probability measures $(\mu_{r,t})_{r,t>0}$ on a compact space metric $X.$

Suppose additionally that:

there exists a probability measure $\mu_{r,0}$ such that $\mu_{r,t}\to^{*,t\to 0}\mu_{r,0}$

and

there exists a probability measure $\mu_{0,0}$ such that $\mu_{r,0}\to^{*,r\to 0}\mu_{0,0}.$

Is it true that there exist the weak* limit of $\mu_{r,t}$ as $r\to 0$ for every $t$ close to $0?$