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This theorem of Tolstoff, proved in 1942, gave the first proof of something claimed by Montel in a 1913 paper.

In the subsequent years, Looman (1923) gave a proof, which, however, contains a serious gap. That mistake has been pointed out by Menchoff (1925) who gave a correct proof of a result weaker than what was claimed by Montel.

It is Tolstoff (1942) that gave the first proof of Montel's claim.