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The Loeb Space of Denumerable Infinite Dimensional Probability Product Measure Spaces 被引量:2

The Loeb Space of Denumerable Infinite Dimensional Probability Product Measure Spaces
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摘要 Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning. Let {(Xi, Si, μi) : i ℃ N} be a sequence of probability measure spaces and (*Xi, L(*Si), L(*μi)) be the Loeb measure space with respect to (Xi, Si, μi) for i ℃ N. Let X =× Xi, S = ×Si,μ = ×μi. We prove that × L(*Si) CL(*S) and in embedding meaning.
作者 陈东立
机构地区 School of Science
出处 《Northeastern Mathematical Journal》 CSCD 2003年第3期249-253,共5页 东北数学(英文版)
基金 The Special Science Foundation (00jk207) of the Educational Committee of Shaanxi Province.
关键词 denumerable infinite dimensional product measure space Loeb measure space internal set external set denumerable infinite dimensional product measure space, Loeb measure space, internal set, external set
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  • 1Cutland, N. J., Nonstandard measure theory and its applications, Bull. London Math.Soc., 15(1983), 529-589.
  • 2Paul, H. R., Measure Theory, Springer-Verlag, New York, 1974.
  • 3Davis, M., Applied Nonstandard Analysis, Wiley, New York, 1977.

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