Actually I know that if the integral of a non negative function is equal to zero then that function is equal to zero almost everywhere. Can I use that to prove or is there a counterexample for my above problem? Note by integral I mean Lebesgue integral.
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$\begingroup$ Lebesgue, incidentally. (For a counter-example, consider e.g. $\int_{\mathbb{R}} \frac{dx}{1+x^2} = \int_{\mathbb{R}} \mathbf{1}_{[0,\pi]}(x)dx$.) $\endgroup$– Clement C.May 29, 2015 at 13:36
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$$\int_0^1 \frac{1}{2} \ dx = \int_0^1 x \ dx$$
