Real Analysis Exchange

The Weak Integral by Partitions of Unity

Redouane Sayyad

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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

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

First available in Project Euclid: 27 June 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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