I was wondering : if $f,g$ are two function $L^1$ (or Riemann integrable function), is $fg$ necessarily $L^1$ (or Riemann integrable) ? I would say yes, but I can't prove it. Any idea ?
2026-04-04 03:53:23.1775274803
If $f,g\in L^1$ does $fg\in L^1$?
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Hint
What do you think if $$f(x)=g(x)=\frac{1}{\sqrt x},$$ on $(0,1]$ ?