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Let $(a_n)_{n \ge 1}$ be a sequence of complex numbers, and suppose that the sequence has a well-defined "average", in the sense that $$ \lim_{N \to \infty} \frac{1}{N}\sum_{i = 1}^N a_i = R$...

I encountered this statement about Dirichlet series but couldn't find a similar result in Korevaar's "Tauberian Theory". Is this statement valid? Statement: Let $f(s) = \sum_{n=1}^{\infty} \...