23 | 11 | 2017

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Article 52

Perron*-Ridder and Denjoy*-Ridder  type integrals

(Unpublished)

Mathematical reviews subject classification: 26A39, 26A45, 26A46, 26A30.

 

Abstract

The Hake-Alexandroff-Looman Theorem asserts that the restricted Denjoy integral is equivalent to the classical Perron integral (see S. Saks, Theory of the integral, 2nd. rev. ed., vol. PWN, Monografie Matematyczne, Warsaw, 1937, pp. 247-252).

In this paper we introduce a general Perron*-Ridder type integral AincP*, and a general Denjoy*-Ridder type integral AD*, and study some of their basic properties.

Then we show that the two integrals are equivalent, i.e. a Hake-Alexandroff-Looman type theorem.

 

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