Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  578.30018
Autor:  Edrei, A.; Erdös, Paul
Title:  Entire functions bounded outside a finite area. (In English)
Source:  Acta Math. Hung. 45, 367-376 (1985).
Review:  Problem: Under what circumstances can it happen that for an entire function f(z) the 2-dimensional Lebesgue measure of {z: |f(z)| > B} is finite for some positive B? The authors answer this problem completely by proving that this can only happen, if

lim infr ––> oo log log log M(r)/ log r \geq 2.

An example shows that 2 can not be replaced by a larger number.
Reviewer:  W.H.J.Fuchs
Classif.:  * 30D20 General theory of entire functions
                   30D35 Distribution of values (one complex variable)
Keywords:  Lebesgue measure

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