I need to know whether, under some assumptions about the functions behavior , and maybe some values of integration limits $a,b$, the following relation holds:
$\int_a^bdx \ f(x) = \int_a^b dx \ g(x) \rightarrow f(x) = g(x)$
I think there was a theorem about it, not sure if when $(a=0, \ b=\infty)$ or maybe it was when it holds for every $a$ and $b$ values. I was looking on the internet but I could not find it
I would like to know whether is some possibility to write this
$\int_0^\infty dx \ f(x) = \int_0^\infty dx \ g(x) \rightarrow \int_0^\infty dx \ f(x)h(x) = \int_0^\infty dx \ g(x)h(x) $
Thanks in advance!