| 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. |
