I am studying measure theory, and I came across the following problem:
Let $f: [a, b]\to (0, \infty)$ be continuous, and let $ G = \{ (x, y): y = f(x)\}.$ Prove that $G$ is measurable only if $f$ is differentiable in $(a, b)$.
I am studying measure theory, and I came across the following problem:
Let $f: [a, b]\to (0, \infty)$ be continuous, and let $ G = \{ (x, y): y = f(x)\}.$ Prove that $G$ is measurable only if $f$ is differentiable in $(a, b)$.