Spaceability and algebrability of the set of non strongly McShane (product) integrable functions

Ali Farokhinia, Fatemeh Farmanesh

Abstract


Let X be a unitial Banach algebra, G be the set of functions f : [0, 1] → X that are non strongly McShane integrable and L be the set of functions f : [0, 1] → [0, ∞) that are non strongly McShane integrable. The aim of this paper is to show that there is an infinite dimensional closed vector space in G ∪0 and a c-generated algebra in L isomorphic with a free algebra.

Keywords


Spaceability, Algebrability, McShane integrable, Product integrable

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