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This is the fifth part in a series of papers in which we introduce anddevelop a natural, general tensor category theory for suitable modulecategories for a vertex (operator) algebra. In this paper (Part V), we studyproducts and iterates of intertwining maps and of logarithmic intertwiningoperators and we begin the development of our analytic approach.

Logarithmic tensor category theory, V: Convergence condition for intertwining maps and the corresponding compatibility condition