The definition of a strict sense stationery random process is given as follows:
Formally, let {${X_t}$} be a stochastic process and let $F_{{X}}(x_{{t_{1}+\tau }},\ldots ,x_{{t_{k}+\tau }})$ represent the cumulative distribution function of the joint distribution of {$X_t$} at times ${t_{1}+\tau ,\ldots ,t_{k}+\tau }$. Then, {$X_t$} is said to be strictly (or strongly) stationary if, for all $k$, for all $\tau$, and for all ${t_{1}+\tau ,\ldots ,t_{k}+\tau }$,
$F_{{X}}(x_{{t_{1}+\tau }},\ldots ,x_{{t_{k}+\tau }})$=$F_{{X}}(x_{{t_{1} }},\ldots ,x_{{t_{k} }})$
Now my doubt is that how are we infering properties about a function defined on an uncountable set w.r.t. 't' by just observing countable number of samples of that function?
Is there anything more general which checks for uncountable points?