I'm currently reading a book on probability theory (Resnick, "A Probability Path") and in a section on basic set and measure theory, the indicator function is defined as follows:
and some properties are discussed, including:
for which it is stated: "and if the sequence is mutually disjoint, then equality holds."
However, I don't understand this: the LHS can only ever be 0 or 1, whereas the RHS can be any integer between 0 and the total number of subsets. How could equality ever hold except under specific cases?
Update: Actually, I just realised I'm being stupid. If the sets are disjoint, then the RHS would also only return 0 or 1.
Any pointers greatly appreciated!