The Closed Graph Theorem and the Space of Henstock-Kurzweil Integrable Functions with the Alexiewicz Norm
We prove that the cardinality of the space ℋ𝒦([a,b]) is equal to the cardinality of real numbers. Based on this fact we show that there exists a norm on ℋ𝒦([a,b]) under which it is a Banach space. Therefore if we equip ℋ𝒦([a,b]) with the Alexiewicz topology then ℋ𝒦([a,b]) is not K-Suslin, neither in...
Main Authors: | Luis Ángel Gutiérrez Méndez, Juan Alberto Escamilla Reyna, Maria Guadalupe Raggi Cárdenas, Juan Francisco Estrada García |
---|---|
Format: | Article |
Language: | English |
Published: |
Hindawi Limited
2013-01-01
|
Series: | Abstract and Applied Analysis |
Online Access: | http://dx.doi.org/10.1155/2013/476287 |
Similar Items
-
Henstock-Kurzweil Integral Transforms
by: Salvador Sánchez-Perales, et al.
Published: (2012-01-01) -
The Use of an Isometric Isomorphism on the Completion of the Space of Henstock-Kurzweil Integrable Functions
by: Luis Ángel Gutiérrez Méndez, et al.
Published: (2013-01-01) -
The Henstock–Kurzweil Integral
by: David, Manolis
Published: (2020) -
A Fubini Theorem in Riesz spaces for the Kurzweil-Henstock Integral
by: A. Boccuto, et al.
Published: (2011-01-01) -
Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions
by: D. A. León-Velasco, et al.
Published: (2019-01-01)