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Then the Lebesgue measure of the Julia set $J(p_a)$ is equal to zero.\n  As part of the proof we discuss a property of the critical point to be {\\it persistently recurrent}, and relate our results to corresponding ones for real one dimensional maps. In particular, we show that in the persistently recurrent case the restriction $p_a|\\omega(0)$ is topologically minimal and has zero topological entropy. 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