复Loeb测度空间中的Radon-Nikodym定理

Radon-Nikodym Theorem in Complex Measure Space

在非标准多饱和模型下,讨论了复Loeb测度空间中的Radon-Nikodym定理.首先,给出了复测度及其变差相应的Loeb测度之间的关系.其次,给出了有限测度的复Loeb空间中的Radon-Nikodym定理.最后,得到了?-有限测度的复Loeb空间中的Radon-Nikodym定理.

In nonstandard polysaturated model,Radon-Nikodym theorem is discussed in complex Loeb measure space.Firstly,it shows the relations between the complex measure and corresponding Loeb measures.Then,Radon-Nikodym theorem on finite measure is proved in complex Loeb measure space.Finally,Radon-Nikodym theorem on σ-finite measure is also obtained.