Addendum to my paper `The Lebesgue summability of trigonometric integrals" (J. Math. Anal. Appl. 390 (2012), 188-196)

We observed that statement (2.9) in Theorem 2 remains valid if condition (2.7) is replaced by the weaker condition that $$f(t)\in L^1(-T,T)\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}T>0.\text{eqno}({2.7}^{\mathrm{\prime }})$$