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Martin Sleziak
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Reference needed for proof of a Tauberian theorem

I was reading the following paper by Hubert Delange: http://www.numdam.org/article/ASENS_1956_3_73_1_15_0.pdf 1. In page 26, he provides a proof of Theorem b, the bulk of which relies on a result in some reference provided by him in footnote 5. However, despite my best attempts, I have been unable to find the aforementioned reference. Any proof or reference with a complete proof of the theorem would be really appreciated. Thanks a lot.

1Delange, Hubert, Sur la distribution des entiers ayant certaines propriétés, Ann. Sci. Éc. Norm. Supér., III. Sér. 73, 15-74 (1956). ZBL0072.27501, MR0083519.

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