Real Analysis Exchange

From Scalar McShane Integrability to Pettis Integrability

M. Saadoune and R. Sayyad

Full-text: Open access

Abstract

A new concept of McShane-tightness is introduced to pass from scalar (alias weak) McShane integrability to Pettis integrability. It is used also to derive a scalar McShane version of the Vitali theorem.

Article information

Source
Real Anal. Exchange, Volume 38, Number 2 (2012), 445-466.

Dates
First available in Project Euclid: 27 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1403894904

Mathematical Reviews number (MathSciNet)
MR3261889

Zentralblatt MATH identifier
1298.28028

Subjects
Primary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 26A04
Secondary: 26A39: Denjoy and Perron integrals, other special integrals

Keywords
McShane integral Pettis integral scalar McShane integral locally \(\tau\)-upper McShane-bounded locally McShane-tight

Citation

Saadoune, M.; Sayyad, R. From Scalar McShane Integrability to Pettis Integrability. Real Anal. Exchange 38 (2012), no. 2, 445--466. https://projecteuclid.org/euclid.rae/1403894904


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