Question: A function \(f: \mathbb{R}^{d} \rightarrow R\) is lower semicontinuous (l.s.c.) if \(\liminf _{y \rightarrow x} f(y) \geq f(x)\) for all x. A function is upper semicontinuous (u.s.c.) if \(\lim \sup _{y \rightarrow x} f(y) \leq f(x)\) for all \(\mathrm{x} .\) Show that, if \(f\) is l.s.c. or u.s.c., then \(f\) is measurable.

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