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**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** **inf**_{r ––> 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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