Order-boundary characterization of the linear lattice of Riemann \(\mu \)-integrable functions as a certain completion of the linear lattice of bounded continuous functions

DOI10.1090/spmj/1822MaRDI QIDQ6633320

Valeriy K. Zakharov

Publication date: 5 November 2024

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

characterizationtightnesscompletionRadon measuretopological spacecontinuous functionsorder boundsRiemann extensionRiemann integrable functions

Mathematics Subject Classification ID

Ordered topological linear spaces, vector lattices (46A40) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15)

Cites Work

• Classical extensions of a vector lattice of continuous functions
• Sets, functions, measures. Volume 1: Fundamentals of set and number theory
• Sets, functions, measures. Volume 2: Fundamentals of functions and measure theory
• On an inner characteristic of the set of all continuous functions defined on a bicompact Hausdorff space.
• Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions.)
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