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 $$f(t) \in L^1(-T, T) \quad {\rm for\ all} \quad T>0.\eqno(2.7')$$ 
Ferenc Moricz
math.CA