Taiwanese Journal of Mathematics

Searching for Structures Inside of the Family of Bounded Derivatives Which are not Riemann Integrable

Pablo Jiménez-Rodríguez

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We construct a non-separable Banach space every nonzero element of which is a bounded derivative that is not Riemann integrable. This in particular improves a result presented in [3], where the corresponding space was found to be separable.

Article information

Taiwanese J. Math., Volume 22, Number 6 (2018), 1427-1433.

Received: 3 December 2017
Accepted: 13 April 2018
First available in Project Euclid: 18 April 2018

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Zentralblatt MATH identifier

Primary: 15A03: Vector spaces, linear dependence, rank 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 26A42: Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX] 47L05: Linear spaces of operators [See also 46A32 and 46B28]

lineability spaceability derivatives Riemann integrability


Jiménez-Rodríguez, Pablo. Searching for Structures Inside of the Family of Bounded Derivatives Which are not Riemann Integrable. Taiwanese J. Math. 22 (2018), no. 6, 1427--1433. doi:10.11650/tjm/180403. https://projecteuclid.org/euclid.twjm/1524038539

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