Real Analysis Exchange

Hake-Alexandroff-Looman Type Theorems

Vasile Ene

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In this paper we shall study three kinds of descriptive type integrals, that all generalize the wide Denjoy integral. In fact the classes of primitives for these integrals, restricted to the continuous functions, are \(ACG\). We shall also study five kinds of Perron type integrals, that are all in a close relationship with the descriptive type integrals. In the last three sections we show some relationships between the descriptive type integrals and the Perron type integrals.

Article information

Real Anal. Exchange, Volume 23, Number 2 (1999), 491-524.

First available in Project Euclid: 14 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 26A39: Denjoy and Perron integrals, other special integrals 26A45: Functions of bounded variation, generalizations 26A46: Absolutely continuous functions

{\(ACG\)} {\(VBG\)} {Lusin's condition \((N)\)} {Foran's condition \((M)\)} {nonabsolutely convergent integrals}


Ene, Vasile. Hake-Alexandroff-Looman Type Theorems. Real Anal. Exchange 23 (1999), no. 2, 491--524.

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