Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $f(x)$ be a real measurable function defined on $[a,b]$. Let $n(y)$ be the number of solutions of the equation $f(x) =y$. Prove that $n(y)$ is a measurable function on $\mathbb{R}$. Considering f(x)=a is measureable and discuss the counting measure of it?

share|cite|improve this question
Are you allowing the possibility that $n(y) = +\infty$? – Greg Martin Dec 12 '12 at 18:39
@GregMartin I have not consider that.But I think it should make no difference. – Jebei Dec 12 '12 at 18:41

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.