Using functions of bounded variation, we define a Volterra type derivative of the linear functional associated with a Lebesgue integrable function and show that it is equal to this function almost ...

Banach spaces and integrability theory are fundamental areas in functional analysis, focusing on the properties of functions and their integrals within certain mathematical structures. Banach spaces ...

The purpose of this paper is to present Fatou type results for a sequence of Pettis integrable functions and multifunctions. We prove the non vacuity of the weak upper limit of a sequence of Pettis ...

Banach spaces, as complete normed vector spaces, provide a fundamental setting in modern analysis, allowing for a rigorous treatment of convergence and stability in infinite dimensions. Integrability ...