Let \(X=\left\\{x_{1}, x_{2}, \ldots\right\\}\) be any countable set, and let
\(p_{1}, p, \ldots\) be positive numbers such that
$$
\sum_{n=i}^{\infty} p_{n}=1
$$
On the set \(\mathscr{S}_{\text {? }}\) of all subsets of \(\mathrm{X}\), define a
measure \(\mu\), by the formula
$$
\mu(A)=\sum_{x_{\mathrm{s}} \in A} p_{n} \quad(A \subset X)
$$
where the sum is over all \(n\) such that \(x_{n} \in A\). Prove that \(\mu\) is a
o-additive measure, with \(\mu(X)=1\).
