An extension of the usual problem of bounding the total variation of the difference of two probability measures is considered for certain convolutions of probability measures on a measurable Abelian group. The result is a fairly general approximation theorem which also yields an $L_p$ approximation theorem and a large deviation result in some special cases. A limit theorem in equally general setting is proved as a consequence of the main theorem. As the convolutions of probability measures under consideration reduce to the Poisson binomial distribution as a special case, an alternative proof of the approximation theorem in this special case is discussed.
"An Approximation Theorem for Convolutions of Probability Measures." Ann. Probab. 3 (6) 992 - 999, December, 1975. https://doi.org/10.1214/aop/1176996224