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We show that if f_t is a holomorphic family of quadratic-like maps with allperiodic orbits repelling so that for each real t the map f_t is a realCollet-Eckmann S-unimodal map then, writing m_t for the unique absolutelycontinuous invariant probability measure of f_t, the map t -> \int g dm_t isreal analytic for any real analytic function g.

Analyticity of the SRB measure for holomorphic families of quadratic-like Collet-Eckmann maps