Riemann integrability and Lebesgue measurability of the composite function
type: Item
instance of: scholarly article
title: Riemann integrability and Lebesgue measurability of the composite function
zbMATH Open document ID: 1171.26005
author: Daniel Azagra
author: G. A. Muñoz-Fernández
author: J. B. Seoane-Sepúlveda
author: Victor Sanchez
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-05-13T00:00:00Z
review text: The authors construct a \(2^c-\)dimensional linear space \(V\) of real-valued Riemann integrable functions on \(\mathbb{R}\) and a \(c-\)dimensional linear subspace \(W\) of \(C[0,1]\) such that for every \(f\in V\setminus\{0\}\) and every \(g\in W\setminus\{0\}\) the function \(f\circ g\) is not Riemann integrable. Moreover, they construct a \(c-\)dimensional subspace \(W\) of \(C[0,2]\) with the following property: For every \(g\in W\setminus \{0\}\) there exists a \(c-\)dimensional space \(V\) of measurable functions such that \(f\circ g\) is not measurable for all \(f\in V\setminus \{0\}\).
reviewed by: Hans Weber
Mathematics Subject Classification ID: 26A42
Mathematics Subject Classification ID: 28A20
zbMATH DE Number: 5553669
zbMATH Keywords: Riemann integrable function
zbMATH Keywords: Lebesgue measurable function
zbMATH Keywords: lineability
zbMATH Keywords: spaceability
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.12.033
OpenAlex ID: W1970347657
cites work: Q4793616
cites work: Lineability and spaceability of sets of functions on $\mathbb {R}$
cites work: Algebrability of the set of non-convergent Fourier series
cites work: Q4488051
cites work: Lineability and algebrability of pathological phenomena in analysis
cites work: Vector spaces of non-measurable functions
cites work: Q5732756
cites work: Q5577487
cites work: On lineability of sets of continuous functions
cites work: Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions
cites work: Is the Composite Function Integrable?
cites work: Lineability in subsets of measure and function spaces
cites work: Bounded linear non-absolutely summing operators
DOI: 10.1016/J.JMAA.2008.12.033
description: scientific article; zbMATH DE number 5553669