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Journal of the London Mathematical Society 1995 52(3):517-528; doi:10.1112/jlms/52.3.517
© 1995 by London Mathematical Society
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© The London Mathematical Society

Minimal Fine Limits of Subharmonic Functions of Slow Growth

K. F. Barth and P. J. Rippon

Syracuse University Syracuse, New York 13244, USA
The Open University Walton Hall, Milton Keynes MK7 6AA

Received 28 January 1994. Revision received 16 May 1994.

Two results are proved which show that a subharmonic function on the unit disc which does not grow too quickly and which does not have asymptotic value {infty} at too many points, must have finite minimal fine limits at boundary points forming a set of positive linear measure. Similar methods are used to obtain an asymptotic Phragmén-Lindelöf theorem for subharmonic functions. These results generalize and improve on earlier results for holomorphic functions.


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