On the relation between Lebesgue summability and some other summation methods

It is shown that if∑n=1Nn|cn|=O(N), then Lebesgue summability, (C,β) summability (β>0), Abel summability, Riemann summability, and (γ,κ) summability (κ⩾1) of the series ∑n=0∞cn are all equivalent to one another.