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The Study of Representation and Some Corresponding Questions of the LOEB Measure

Author: HanZuo
Tutor: ChenDongLi
School: Xi'an University of Architecture and Technology
Course: Applied Mathematics
Keywords: Non-standard model Loeb measure σ-algebra Inverse standard part mapping
CLC: O174.12
Type: Master's thesis
Year: 2010
Downloads: 10
Quote: 0
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Abstract


Loeb measure theory based on nonstandard κ- saturated model , discuss some properties of the inverse standard part mapping gives a definition of the standard measure outside the Loeb measure , to discuss what measures can be \(partial map) Loeb prove certain properties of the aggregate functions , focuses on the use of the Loeb measure portrayed measure several methods first introduced in the first , the second chapter , the background and development of nonstandard analysis generated and nonstandard analysis theory outlined and discussed the relationship between the standard global and non-standard global , non-standard model and some properties of the final study . third chapter introduces Loeb measure kinds of construction method , prove that the two different ways to construct the Loeb measure space is consistent . Loeb measurable function on this basis , research Loeb integral theory. fourth chapter first discusses the inverse standard part mapping of some of nature ; Secondly, the concept of standard measure μ outer Loeb measure υ · φ μ outer Loeb measure represented a necessary and sufficient condition ; then given a measure by \the definition to discuss what measures can be \X is a regular space, and u is sub- additive and can be added within a collection of functions , then υ · st-1 τ- smooth Borel measure .

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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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