Real Analysis Exchange

The Weak Integral by Partitions of Unity

Redouane Sayyad

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Abstract

We introduce the notion of the the weak integral by partitions of unity for functions defined on a \(\sigma\)-finite outer regular quasi Radon measure space \((S,\Sigma,\mathcal{T},\mu)\) into a Banach space \(X\) and discuss its relation with the weak McShane integral which has been introduced by M. Saadoune and R. Sayyad (2014).

Article information

Source
Real Anal. Exchange, Volume 44, Number 1 (2019), 181-198.

Dates
First available in Project Euclid: 27 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.rae/1561622439

Digital Object Identifier
doi:10.14321/realanalexch.44.1.0181

Mathematical Reviews number (MathSciNet)
MR3951341

Zentralblatt MATH identifier
07088970

Subjects
Primary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22]
Secondary: 26A39: Denjoy and Perron integrals, other special integrals

Keywords
Pettis integral McShane integral Weak McShane integral PU-integral Weak PU-integral

Citation

Sayyad, Redouane. The Weak Integral by Partitions of Unity. Real Anal. Exchange 44 (2019), no. 1, 181--198. doi:10.14321/realanalexch.44.1.0181. https://projecteuclid.org/euclid.rae/1561622439


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