%0 Journal Article
%A D'Aniello, E.
%A Fernández Sánchez, Juan
%A Maiuriello, M.
%A Seoane Sepúlveda, Juan Benigno
%T Algebrability and Riemann integrability of the composite function
%D 2024
%U https://hdl.handle.net/20.500.14352/130482
%X 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.
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