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I am working on infinite products. I found the following definition for convergence of infinite products in Wikipidea.

The product of positive real numbers $\prod_{n=1}^\infty a_n$ converges to a non zero real number if and only if the sum $\sum_{n=1}^\infty \ln(a_n)$ converges.

However, I am looking for any standard references, such as books or journals, to cite the definition. Could you name few books or journals which define the convergence of infinite products?

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    What you've cited, I would call a theorem, not a definition. – 2017-02-23

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Any reasonably advanced book on complex analysis should cover this. E.g. Jones and Singerman, Complex Analysis: an algebraic and geometric viewpoint, p. 83ff. A more standard text is Alfors, Complex Analysis, where you want p. 189ff.