单子集映射m_τ与标准部分逆映射st^(-1)的同态性

The Homomorphism of Monadic Set-mapping m_T and Standard Part Inverse Mapping st^(-1)

在饱和模型中,讨论了单子集映射m_T及标准部分逆映射st^(-1)的同态性质.证明了m_T能扩张成一个σ-同态的充要条件是X是可数紧空间.在一定条件下,st^(-1)是Borelσ-代数上的σ-同态映射,当且仅当X是预Hausdorff的,并给出了一个正则测度的一个Loeb表示.

In nonstandard saturated model,the properties of the homomorphism of monadic set-mapping m_T and standard part inverse mapping si^（-1） are discussed.It is proved that a sufficient and necessary condition,under which m_T can be extened to a cr-homomorphism,is that the space X is countably compact.Under some conditions,it is obtained that st^（-1） is aσ-homomorphic mapping on Borel cr-algebra,if and only if the space X is pre-Hausdorff.Finally, Loeb representation of a regular measure is shown.