How to denote a set of functions Say there is an unknown function $h(x)$ $$\int_A^B h(x) = c$$ $A$, $B$ and $c$ are known. So $h(x)$ can have various forms on the range $[A,B]$. I want to know how to denote the set of functions for $h(x)$. I know the notation for a set is $\{...\}$.
So would it be: $\{h(x)|\int_A^B h(x) = c\}$? Or is there a different way to refer to a bunch of different possible functions?
I intend to narrow down this set by gradually introducing boundary restrictions/conditions. E.g. $h(x) \in \mathbb R$ and $h(x) = f(x)\cdot g(x)$ with $g(x)$ known.  

Summarizing the comments: try 


*

*$\{h \in C([A,B])\vert\int_A^B h(x)\,dx = c\}$ or 

*$\{h \in L^1([A,B])\vert\int_A^B h(x)dx = c\}$


depending on what kind of functions you consider. Simply saying functions with integral equal to $3$ is usually ambiguous: there are different kinds of integrals.
Avoid writing $h(x)$ when you mean $h$. 
