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We observed that statement (2.9) in Theorem 2 remains valid if condition(2.7) is replaced by the weaker condition that $$f(t) \in L^1(-T, T) \quad {\rmfor\ all} \quad T>0.\eqno(2.7')$$

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