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关于σ^--有限测度空间的Loeb空间的一点注记 被引量:3

The Loeb Spaces of σ^--finite measure spaces
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摘要 以一种自然的方式定义了σ-有限测度空间的 L oeb空间 ,并研究了其若干性质 .将有限 L oeb测度空间的一些重要性质推广到σ-有限情形 ,并将 L oeb测度对有限 The Loeb Space of σ finite measure space is defined in natural way. Some properties of it are studied. Some important properties of finite Loeb measure space are generalized to σ finite situation. The theorem about the representation of Radon space by Loeb space is also generalized to σ finite situation.
作者 陈东立
出处 《数学研究》 CSCD 2002年第3期294-297,共4页 Journal of Mathematical Study
基金 陕西省教育厅专项科研基金项目 (0 0 jk2 0 7)
关键词 σ-有限测度空间 Loeb测度空间 提升 RADON测度 finite measure space σ finite measure space Radon space Lifting S integrable
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参考文献4

  • 1Cutland N J. Nonstandard Measure Theory and its applications, Bull. London Math. Soc. 1983, 15:529~589
  • 2Landers D, Logge L. Universal Loeb-measurablity of Sets and of the Standard Part Map with Applications. Trans. Amer. Math. Soc. 1987, 304:229~243
  • 3Cohn D L. Measure Theory, Birkauser Boston, 1980
  • 4Davis M. Applied Nonstandard Analysis, Wiley, New York, 1977

同被引文献15

  • 1刘普寅,金治明.Radon概率空间中随机过程到Loeb概率空间中的转换[J].高校应用数学学报(A辑),1998,13(4):433-442. 被引量:6
  • 2祁明,刘建民.关于乘积Loeb空间上的集合泛可测性的若干结果[J].工程数学学报,1993,10(3):90-94. 被引量:1
  • 3陈东立,冯汉桥.广义Loeb测度及像Loeb测度的性质[J].陕西师范大学学报(自然科学版),1996,24(4):110-111. 被引量:4
  • 4Cutland N J. Nonstandard measure theory and its application [J]. Bull London Mathematical Society, 1983, 15( 1 ) : 526 -589.
  • 5Cohn D L. Measure theory[M]. Boston: Birkhauser, 1980.
  • 6Landirs D, Rogge L. Universal Loeb measurability of sets and of standard part map with applications [ J ]. Trans Amer. Math. Soc, 1987,304 : 229 - 243,.
  • 7S. Albeverio. J. E. Fenstad, R. Hoegh - Krohn, and T. Lindstrom. Nonstandard methods in stochasitic analysis and mathematical physics [ M ]. New York:Academic Press,1986.
  • 8CUTLAND N J.Nonstandard measure theory and its application[J].Bull London Mathematical Society, 1983,15(1 ):526-589.
  • 9LANDIRS D, ROGGE L.Universal Loeb measurability of sets and of standard part map with applications[J].Trans Amer. Math.Sot, 1987,304:229-243.
  • 10COHN D L.Measure theory[M].Boston:Birkhauser, 1980:24-25.

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