Functiones et Approximatio Commentarii Mathematici

A convergence theorem for the Birkhoff integral

Marek Balcerzak and Kazimierz Musiał

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Abstract

We propose an essential improvement of a convergence theorem for the Birkhoff integral. We also obtain the respective version of this result for the convergence associated with an ideal on $\mathbb N$.

Article information

Source
Funct. Approx. Comment. Math., Volume 50, Number 1 (2014), 161-168.

Dates
First available in Project Euclid: 27 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.facm/1395924289

Digital Object Identifier
doi:10.7169/facm/2014.50.1.5

Mathematical Reviews number (MathSciNet)
MR3189505

Zentralblatt MATH identifier
1292.28006

Subjects
Primary: 11K06: General theory of distribution modulo 1 [See also 11J71]
Secondary: 11K38: Irregularities of distribution, discrepancy [See also 11Nxx] 11K41: Continuous, $p$-adic and abstract analogues

Keywords
convergence theorems for integrals Pettis integral Birkhoff integral

Citation

Balcerzak, Marek; Musiał, Kazimierz. A convergence theorem for the Birkhoff integral. Funct. Approx. Comment. Math. 50 (2014), no. 1, 161--168. doi:10.7169/facm/2014.50.1.5. https://projecteuclid.org/euclid.facm/1395924289


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References

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