Notation: is there a symbol for "not a function of"?

Question

For example, let's say a term $A(x,y)$, a function of two random variables $x$ and $y$, is the argument of an expectation over $y$. The resulting term is no longer a function of $y$. Is there a mathematical symbol that explicitly says this?

I know there are workarounds--in this arbitrary case, bar notation and dropping $y$ from the parentheses--but I'm wondering if there's a more concise and explicit way to write this. I have nothing against doing it in words instead of symbols; I'm just curious.

Answer 1

As Git Gud commented, there is a problem with the concept of a "function of variable". However, let $A$ be the set of all possible values of y (that you want to consider), and $B$ be the target set, such that $f$ would be a function $A\rightarrow B$. The set of all functions of a set $X$ into a set $Y$ is commonly denoted as $Y^X$. Therefore, you could write your statement as $f\not\in Y^X$.

If, however, the correct interpretation of "$f$ is not a function of $y$" is the one described by Eike Schulte in the comments on this answer, then I think that what you want to write is $$A(x,y_1) = A(x,y_2) \;\;\;\forall y_1,y_2\in B.$$

Answer 2

You want to express that the function is independent of a certain $y$, so it doesn't change when $y$ changes. I think, in your case derivative would be useful to state this independence:

$\frac{\partial A}{\partial y} = 0$