Is there a notation for "percent of items in set $S$ equal to $x$"?

Question

Given a set, $S$, I'd like to mark the percent of $S$'s member that are equal to $x$.

Something like $\%_x(S)=0.12$.

Is there a conventional short symbol for this, specifically in the statistics domain?

Answer 1

There is a notation for an element to equal a specific value using indicator functions.

You could thus define the proportion equal to $x$ as follows $$ p_x=\frac{1}{N} \sum_{s \,\in\, S}I(s=x) $$ Here $N$ is the number of elements in $S$ and $I$ is the indicator function that equals $1$ when $s=x$ and zero otherwise.

There should be no problem using your own notation (in a paper for example) provided you define it clearly.