An example of a function which is Denjoy integrable but not Khinchin summable

V. S. Shul'man

Mathematics and Mechanics Institute, Academy of Sciences of the Azerbaidzhan SSR

Abstract: The following result is proven: if $\xi$ is irrational number “anomalously badly” approximable by rationals, then there are functions which are not Khinchin $\xi$-summable but which are Denjoy integrable.

UDC: 517.5

Received: 21.08.1969

 English version: Mathematical Notes, 1971, 10:3, 601–604

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