THE CANTOR-LEBESGUE PROPERTY

If the terms of a trigonometric series tend to zero at each point of a set and if the smallest additive group containing that set has positi ve outer Lebesgue measure, then the coefficients of that series tend t o zero. This result generalizes the well known Cantor-Lebesgue Theorem . Several other extensions of the Cantor-Lebesgue Theorem as well as s ome examples to demonstrate scope and sharpness are also given.