Theory of nonabsolute integration
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 pertainin...
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sg-ntu-dr.10356-203392020-11-01T06:20:22Z Theory of nonabsolute integration Ng, Wee Leng. Lee, Peng Yee National Institute of Education DRNTU::Science::Mathematics::Calculus 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. Doctor of Philosophy 2009-12-14T09:35:12Z 2009-12-14T09:35:12Z 1997 1997 Thesis http://hdl.handle.net/10356/20339 en NANYANG TECHNOLOGICAL UNIVERSITY 100 p. application/pdf |
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DRNTU::Science::Mathematics::Calculus Ng, Wee Leng. Theory of nonabsolute integration |
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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. |
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Lee, Peng Yee |
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Lee, Peng Yee Ng, Wee Leng. |
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Theses and Dissertations |
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Ng, Wee Leng. |
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Ng, Wee Leng. |
title |
Theory of nonabsolute integration |
title_short |
Theory of nonabsolute integration |
title_full |
Theory of nonabsolute integration |
title_fullStr |
Theory of nonabsolute integration |
title_full_unstemmed |
Theory of nonabsolute integration |
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theory of nonabsolute integration |
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2009 |
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http://hdl.handle.net/10356/20339 |
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1683493861966479360 |