RT Journal Article
T1 Algebrability and Riemann integrability of the composite function
A1 D'Aniello, E.
A1 Fernández Sánchez, Juan
A1 Maiuriello, M.
A1 Seoane Sepúlveda, Juan Benigno
AB In this note, we show that there exist a 2c-generated free algebra S ⊂ RR of Riemann integrable functions and a free algebra C ⊂ R[0,1] of continuous functions, having c-generators, such that r ◦ c is not Riemann integrable for any r ∈ S and c ∈ C. This result is the best possible one in terms of lineability within these families of functions and, at the same time, an improvement of a previous result ([6, Theorem 2.7]). In order to achieve our results we shall employ set theoretical tools such as the Fichtenholz-Kantorovich-Hausdorff theorem, Cantor-Smith-Volterra–type sets, and classical real analysis techniques.
PB Springer
YR 2024
FD 2024
LK https://hdl.handle.net/20.500.14352/130482
UL https://hdl.handle.net/20.500.14352/130482
LA eng
NO Prof. J. Fernández–Sánchez would like to dedicate this work to the memory of Antonio Carmona Reche (1962–2024). Prof. J.B. Seoane–Sepúlveda would like to dedicate this work to the memory of his aunt Carmen Sepúlveda Aramburu (1947–2024).
DS Docta Complutense
RD 25 abr 2026