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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 . 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.

asrxiiviii
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