Necessary and sufficient conditions for the existence of boundary values of the modulus of a function that is bounded and analytic in a half-plane

Necessary and sufficient conditions are obtained for the existence of a nontangential limit and of a limit along the normal at a particular point of the boundary for the modulus of a function that is bounded and analytic in a half-plane; the conditions consist in the existence at this point of the derivative and of the symmetric derivative, respectively, of the mass distribution function.
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