In this paper, we first show that if υ is absolutly continuous with respect to μ , i.e., υu , then L( *S, *μ)L( *S, *υ) . We also prove that υμ if and only if L( *υ)...In this paper, we first show that if υ is absolutly continuous with respect to μ , i.e., υu , then L( *S, *μ)L( *S, *υ) . We also prove that υμ 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.展开更多
文摘In this paper, we first show that if υ is absolutly continuous with respect to μ , i.e., υu , then L( *S, *μ)L( *S, *υ) . We also prove that υμ 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.
