Điều kiện đủ chuyển dấu tích phân suy rộng với cận vô hạn qua chuỗi hàm

Abstract

In the theory of series of functions, there is a well-known result that if a series converges uniformly on an interval and these functions are integrable on the interval, then its sum is also an integrable function on the interval. The main purpose of this article is to present a counterexample for an improper integral and the proofs of sufficient conditions for two generalizations of this result for improper integrals in [2].