A radial uniqueness theorem for meromorphic functions

Rippon, P. J.

doi:10.1090/S0002-9939-1982-0660607-2

A radial uniqueness theorem for meromorphic functions
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by P. J. Rippon

Proc. Amer. Math. Soc. 85 (1982), 572-574

DOI: https://doi.org/10.1090/S0002-9939-1982-0660607-2

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Abstract:

A classical theorem of Lusin and Privalov states that a meromorphic function in the unit disc, which has radial limit zero on a set which is both of second category and metrically dense in some boundary arc, must vanish identically. We prove below a radial uniqueness theorem which includes the Lusin-Privalov theorem as a special case and which also generalises the Barth-Schneider-Tse asymptotic analogue of the F. and M. Riesz radial uniqueness theorem. The part of the proof relating to Baire category is disposed of by using the Collingwood maximality theorem.

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