On the Differentiation of Integrals in Measure Spaces Along Filters: II

• Published in: Complex analysis and operator theory Vol. 18; no. 5
• Main Authors: Di Biase, Fausto, Krantz, Steven G.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.07.2024; Springer Nature B.V
• Subjects: Analysis; Constraining; Differentiation; Homomorphisms; Integrals; Magma; Mathematical functions; Mathematics; Mathematics and Statistics; Operator Theory; Filters; 18F99; Differentiation of integrals; Natural transformations; 28A15; Almost everywhere convergence; Liftings; 20N02; Partial magmas; Moore-Smith sequences; The Yoneda lemma; 28A51

Let X be a complete measure space of finite measure. The Lebesgue transform of an integrable function f on X encodes the collection of all the mean-values of f on all measurable subsets of X of positive measure. In the problem of the differentiation of integrals, one seeks to recapture f from its Le...