Abstract: In Cassaigne and Maillot (J Number Theory 83:226?255, 2000) and, later on, in Akatsuka (J Number Theory 129:2713?2734, 2009) the authors introduced zeta Mahler measure functions for multivariate polynomials [Cassaigne and Maillot (J Number Theory 83:226?255, 2000) called them ?zeta Igusa? functions, but we follow here the terminology of Akatsuka (J Number Theory 129:2713?2734, 2009)].We generalize this notion by defining a zeta Mahler measure function ZX (·, f ) : C ?? C, where X is a compact probability space and f : X ?? C is a function bounded almost everywhere in X. We give sufficient conditions that imply that this function is holomorphic in certain domains. ZetaMahler measure functions contains big amounts of information about the expected behavior of f on X. This generalization is motivated by the study of several quantities related to numerical methods that solve systems of multivariate polynomial equations. We study the functions Z(·, 1/ · aff ), Z(·, 1/?norm) and Z(·, JAC), respectively associated to the norm of the affine zeros ( · aff ), the non-linear condition number (?norm) and the Jacobian determinant (JAC) of complete intersection zero-dimensional projective varieties. We find the exact value of these functions in terms of Gamma functions and we also describe their respective domains

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