Missouri Journal of Mathematical Sciences

A Lindelöf Property for Uniformly Normal Families

Richard E. Bayne and Myung H. Kwack

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Abstract

In this note we present a simple new proof for a Lindelöf property for a normal map accessible to advanced undergraduate students. The proof extends the result to uniformly normal families: If $\{ f_n :D \to P^1(\mathbb{C})\}$ is a uniformly normal sequence from the unit disk $D$ in the complex plane ${\bf \mathbb{C}}$ into the Riemann Sphere $P^1(\mathbb{C})$ such that $\lim _{r_n \to 1}f_n(r_n)$ exists for all $ \{r_n\}\subset (0,1),$ then the sequence $\{f_n\}$ has non-tangential limit at $1$.

Article information

Source
Missouri J. Math. Sci., Volume 22, Issue 2 (2010), 130-138.

Dates
First available in Project Euclid: 1 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.mjms/1312233143

Digital Object Identifier
doi:10.35834/mjms/1312233143

Mathematical Reviews number (MathSciNet)
MR2675408

Zentralblatt MATH identifier
1208.30033

Subjects
Primary: 32A10: Holomorphic functions
Secondary: 32A18: Bloch functions, normal functions 32A19: Normal families of functions, mappings

Citation

Bayne, Richard E.; Kwack, Myung H. A Lindelöf Property for Uniformly Normal Families. Missouri J. Math. Sci. 22 (2010), no. 2, 130--138. doi:10.35834/mjms/1312233143. https://projecteuclid.org/euclid.mjms/1312233143


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