Lineability of Denjoy integrable function

Authors

  • Ali Farokhinia Dept. of Math. Shiraz Branch, Islamic Azad University

DOI:

https://doi.org/10.30495/jme.v11i0.503

Keywords:

Lineability, Pathological Properties, Denjoy integrable functions, Lebesgue integrable function

Abstract

Gordon presented an example of a function that is Denjoy integrable but not Lebesgue integrable in the book: The integrals of Lebesgue, Denjoy , Peron and Henstock. This example showed thst, the class of Denjoy integrable functions is larger than the class of Lebesgue integrable functions. We are going to show that the set of Denjoy integrable functions that are not Lebesgue integrable, contains an infinite dimensional vector space.

Author Biography

Ali Farokhinia, Dept. of Math. Shiraz Branch, Islamic Azad University

Assistant Proffesor

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Published

2017-01-13

Issue

Vol. 11

Section

Vol. 11, No. 1, (2017)

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