Lineability of Denjoy integrable function

Ali Farokhinia

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.

Keywords


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

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