Measure of set where holomorphic function is large

complex-analysis analysis entire-functions lebesgue-measure

Solution 1:

This set can have finite measure. See, for example, MR0537357 Golʹdberg, A. A. Sets on which the modulus of an entire function has a lower bound, Sibirsk. Mat. Zh. 20 (1979), no. 3, 512–518, 691. (There is an English translation: Siberian Math. Journal, 20 (1980) 360-364).

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