@BalarkaSen," Let $X_1,X_2,\dots$ be a countable collection of closed subsets of $\mathbb R^k$, and let $a_1,a_2,\dots$ be a sequence of nonnegative numbers such that $\sum_na_n<\infty$. For each $x\in X$, define $$U(x)=\sum_{\{n=1,2,\dots | x\in X_n\}}a_n.$$"
Then $U$ is an upper semi-continuous function.