Radon Nikodym Derivative on Loeb Space
Received:September 06, 1994  
Key Words: absolute continuity   Loeb space   Radon-Nikodym Theorem   Radon-Nikodym derivative.  
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Author NameAffiliation
Chen Dongli Xi′an Univeristy of Architecture and Technology
710055 
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Abstract:
      In this paper, we first show that if 《υ is absolutly continuous with respect to μ , i.e., υ《u , then L( *S, *μ)(?)L( *S, *υ) . We also prove that υ《μ if and only if L( *υ)《L(*μ) and d(L(*υ))/d(L(*μ))= 0( *(dμ/dυ)) . We shall define the Loeb space of σ-finite measure space by a natural way and prove that the results above can be extended to σ-finite measure spaces.
Citation:
DOI:10.3770/j.issn:1000-341X.1997.02.008
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