Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/20339
Title: Theory of nonabsolute integration
Authors: Ng, Wee Leng.
Keywords: DRNTU::Science::Mathematics::Calculus
Issue Date: 1997
Abstract: The main objective of this thesis is to define a nonabsolute integral mea-sure theoretically. More precisely we define an integral of the Henstock type, called the H-integral, on measure spaces with a locally compact Hausdorff topology that is compatible with the measure. Relevant re-sults pertaining to the H-integral are established. In Chapter 1, we define the H-integral and derive the properties that are fundamental to an integral. We describe in Section 1.1 how certain objects in the space are chosen to be generalised intervals and relate the definition to some concrete examples. The H-integral is defined in Sec-tion 1.2 and we prove that it includes the well-known Kurzweil-Henstock integral [18] on the real line. The basic properties that hold true for the H integral, in particular, the Henstock's lemma and the monotone convergence theorem, are derived in Section 1.3.
URI: http://hdl.handle.net/10356/20339
Rights: NANYANG TECHNOLOGICAL UNIVERSITY
Fulltext Permission: restricted
Fulltext Availability: With Fulltext
Appears in Collections:NIE Theses

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