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Some Conditions under Which Sequences of Functions are Uniformly Bounded

Published online by Cambridge University Press:  22 January 2016

D.C. Rung
D.C. Rung*
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania
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After one introduces the theory of normal families in a course in complex analysis, the usual pattern is to give an example of a non-normal family. One of the simplest, of course, is the sequence fn(z) = nz, n = 1,2, ···. The very devastating effect of multiplying by zero insures the required abnormality!

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 33 , November 1968 , pp. 75 - 83
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Tsuji, M., Potential theory in modern function theory, Maruzen, Tokyo, 1959.Google Scholar