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5. Let H = {z ( C | Im(z) > 0} and let HI = HUR be its closure. Let f be a bounded and

5. Let H = {z ( C | Im(z) > 0} and let HI = HUR be its closure. Let f be a bounded and continuous function in H , which is holomorphic in H and such that f(2) is real for all z E R. Prove that f is constant

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