Title of article :
Spaceability and algebrability of the set of non strongly McShane (product) integrable functions
Author/Authors :
Farokhinia, Ali Shiraz Branch, Islamic Azad University, Shiraz, Iran , Farmanesh, Fatemeh Shiraz Branch, Islamic Azad University, Shiraz, Iran
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
Journal title :
Journal of Mathematical Extension(IJME)
