L oeb 条件概率空间

摘要

The conditional probability PA in internal finitely additive probability space (X ,ζ,P) is defined ,and the conditional Loeb probability space ( X ,L(ζ,PA ) ,L( PA ) ) is derived by completion .T hen the Loeb space ( X , L(ζ,P) ,LP ) is derived by completion of internal finitely additive probability space (X ,ζ,P) ,and the conditional probability LP(A) in Loeb space (X ,L(ζ,P) ,LP ) is defined .By dicussing the relationship of these two spaces ,it is proved that L(ζ,PA)= L(ζ,P) ,and for ∀B∈ L(ζ,P) ,L(PA)(B)= LP(A)(B) .%给出了内有限可加概率空间（ X ，ζ，P）上条件概率 PA 的定义，并通过完备化得到条件Loeb概率空间（X ，L（ζ，PA），L（PA））。其次对内有限可加概率空间（X ，ζ，P）完备化，得 Loeb空间（X ，L（ζ，P），LP）。在所得Loeb空间上定义Loeb条件概率LP（A），并讨论这2个空间之间的关系，得出L(ζ,PA)= L(ζ,P),且对∀B∈ L(ζ,P),L(PA)(B)= LP(A)(B)。