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The Study of Some Questions of Metric Space Induced by a Internal Finitely Additive Measure Space

Author: LiuYanYing
Tutor: ChenDongLi
School: Xi'an University of Architecture and Technology
Course: Applied Mathematics
Keywords: Within the limited additive measure Loeb measure Metric space Completeness Divisibility
CLC: O174.12
Type: Master's thesis
Year: 2009
Downloads: 20
Quote: 0
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Abstract


In this paper, nonstandard analysis theory, derived by Loeb measure space metric space based on , derived from the inside finitely additive measure space metric space, and with the concept and some properties of Loeb measure proof of export by the standard measure space measure space and the export of non-standard measure space metric space has a close relationship within finitely additive measure on the basis of this relationship also studied the nature of the export finitely additive measure the non-standard measure space metric space in the first , the second chapter , we first briefly describes the production, development and research status of non-standard analysis , and then gives the theoretical basis of the non-standard analysis and axiomatic nonstandard analysis , and then discuss a non-standard model and saturated model , and gives some properties of the non - standard model and saturated model , some equivalent conditions . In the third chapter , we mainly study the by supremum law and within approximation method in two different ways to construct Loeb measure space , and prove their consistency , and then discuss some basic properties of the of Loeb measurable functions and Loeb integral . Chapter IV , the first measure by Loeb export this standard measure space metric space , followed by a discussion of the completeness and separability of the metric space and the Baire theorem . In the fifth chapter , we focus on the relationship between the derived metric space by a finite measure space and export within finitely additive measure space metric space , and then studied on the basis of this relationship is exported from within finitely additive measure space metric Space .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Real Analysis,Real Variable > Measure Theory
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