Real Analysis Exchange

Hake-Alexandroff-Looman Type Theorems

Vasile Ene

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Abstract

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

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

Dates
First available in Project Euclid: 14 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1337001361

Mathematical Reviews number (MathSciNet)
MR1639960

Zentralblatt MATH identifier
0942.26017

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

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

Citation

Ene, Vasile. Hake-Alexandroff-Looman Type Theorems. Real Anal. Exchange 23 (1999), no. 2, 491--524. https://projecteuclid.org/euclid.rae/1337001361


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