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 ...

Let X be a weakly $Lindel\ddot{o}f$ determined Banach space. We prove that if X is non-separable, then there exist a complete probability space (Ω, Σ, μ) and a ...

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 ...