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 positive outer Lebesgue measure, then the coefficients of that series tend to zero. This result generalizes the well known Cantor-Lebesgue Theorem. Several other extensions of the Cantor-Lebesgue Theorem as well as some examples to demonstrate scope and sharpness are also given.