Abstract
Abstract Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succinct proof given in [A. B. Mukhin, Some necessary and sufficient conditions for the validity of local limit theorems, Dokl. Akad. Nauk USSR 1984, 8, 7–8], we could only prove rigorously a weaker necessary and sufficient condition, with a significantly different formulation. This is the object of this short note.
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