Let $S$ be a finite set. I want to consider measures $\mu$ on $S$ which are constant only when not zero.
As an example, let $S$ be $\{a,b,c,d,e\}$, and take the measure: $\mu(a)=\mu(b)=\mu(e)=1/4,\mu(c)=\mu(d)=0$.
(I'm particularly interested in probability measures with the property above, for example the ones you get from the law of large numbers.)
The question is: do measures like these have a name?
(The same can be done with any measurable set with a fixed base measure.)
These are called discrete measures (being nonzero on a countable set) and Dirac measures (being constant on a set and $0$ everywhere else).