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Seek help to formalize an argument to positiveness of function defined inductively by integral [closed]
I define the induction
$$h(x)=\int_0^x f(t)g(t)h(t) dt$$
I imagine that is possible to say that $h(x)$ (and so $g(x)$) remains positive, but I could not find a formal argument.
Thank you in advance. …