Primitives of Essentially Bounded Henstock-Kurzweil Integrable Functions
Keywords:
Henstock-Kurzweil integral, essentially bounded functionsAbstract
A full descriptive characterization of essentially bounded Henstock-Kurzweil integrable function is given. More precisely, an essentially bounded function on is Henstock-Kurzweil integrable if and only if there exists a function F satisfying the Lipschitz condition on [a,b] with almost everywhere. Some implications were given, including integration by parts, substitution formula and a convergence theorem. These known results were presented and proved using the existing results in the Henstock-Kurzweil integration.
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