# Showing a function is zero a.e [closed]

Let $$g:R\to [0,\infty)$$ is measurable such that $$\int_R g(t)e^{n|t|} dt \leq M$$ for all $$n=1,2,...$$ where $$M$$ is finite. To prove that $$g=0$$ a.e. I have no idea where to start with this problem, any hints will be appreciated.

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• This seems to be (nice) homework. – Dieter Kadelka 2 days ago
• Obviously false as stated. Are there missing quantifiers? – Steven Landsburg yesterday