Assume $f : X \to [0,\infty]$
I want to prove $$\sum_{x \in X} f(x)<\infty \Longrightarrow \{x \in X | f(x) >0\} \text { is a countable set}$$
Is it connected with finite property? Give me some help to prove it.
Assume $f : X \to [0,\infty]$
I want to prove $$\sum_{x \in X} f(x)<\infty \Longrightarrow \{x \in X | f(x) >0\} \text { is a countable set}$$
Is it connected with finite property? Give me some help to prove it.