## A radial uniqueness theorem for meromorphic functions

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- by P. J. Rippon PDF
- Proc. Amer. Math. Soc.
**85**(1982), 572-574 Request permission

## 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.## References

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## Additional Information

- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**85**(1982), 572-574 - MSC: Primary 30D40
- DOI: https://doi.org/10.1090/S0002-9939-1982-0660607-2
- MathSciNet review: 660607