A remark on the behavior of integrable functions at infinity
Abstract
We prove that any continuous function f : [0;1) ! R; for which the integral R10 f(x)/x dx exists at least as a Riemann improper integral, veries the condition lim x!1 1/x Z x 0 f(t)dt = 0.
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PDFDOI: https://doi.org/10.52846/ami.v38i4.448