关键词: absolute continuous, Loeb measure space, denumerable comprehension, over- flow principle, infinitesimal prolongation

Abstract: It is proved that if μ and v be finite measures on a measurable space (X, S) and v is absolutely continuous with respect to v, then it is holds that L(* S, * μ) L(* S, *v), while L(*S, *μ) and L(*S, V) are the Loeb algebras with respect to measure spaces (X, S,μ) and (X,S,v).

Key words: absolute continuous, Loeb measure space, denumerable comprehension, over- flow principle, infinitesimal prolongation