Let $A$ be a set, i.e. $A=\{2,3\}$. Then it is common to denote by $\{f(a)|a\in A\}=\{f(2),f(3)\}$ the result of application of function $f$ on items from $A$.
But this work just for sets. How is this denoted for multisets? Is there some common notation? Have anyone used any notation other than verbal explanation?
For a multiset $B=\{2,2,3\}$ the result should be $\{f(2),f(2),f(3)\}$.
Most of the time, one uses indexed families instead of multisets. Then the application of a function $f$ on an indexed family $(a_i)_{i \in I}$ (or $\{a_i\}_{i \in I}$ if that is the notation one prefers) can be simply expressed as $(f(a_i))_{i \in I}$ (or $\{f(a_i)\}_{i \in I}$).