摘要
测度论中的Radon—Nikodym定理是初等微积分中Neuton—Leibnitz定理的推广,在向量测度论中RN定理对一般Banach空间不必成立,如C_0,L(μ)等。本文将向量测度G:∑→X的RN导数g∈L(μ,X)代之以g∈L(μ,x),因为实数域R与复域c都是自共扼(更是自反)的Banach空间,所以这种推广也是自然的。这里我们证明了广RN定理在有尾缩基(shrinkingbasis)的B—空间成立,因而Co有广RNP,因L(μ)对任何偶次共扼扩充的RN定理都不成立。所以Co与L(μ)在RNP分类中是本质不同的。本文也证明了空间X有广RNP与每个算子T:L(μ)→X的广Riesz可表示的等价性。
The Radon-Nikodym theorem in measure theory is the generalization of Newton-Leibnitz theorem in elementary differential and integral calculus, but in the vector measure, is it not necessary for the Radon-Nikodym theorem to be tenable for general Banach spaces,such as Co. L(μ) ,etc. In this papet, g∈L(μ,X* * ) is used to replace RN derivative g∈ L(μ,X) of vector measures G: ∑ - X. Since the real field R and the complex field C are both self - conjugate (reflexive moreover) Banach spaces,this generalization is natural. Thus we prove that the generalized RN theorem holds what in B-space with shrinking basis, therefore Co has generabzed RNP. As L(μ) is not tenableor RN theorem with even conjugate extesion,Co is different essentially from L(μ) in the RNP partition. The paper also testifies that-space X has a representaive equivalency between generalized RNP and the generlized Riesz of every operator T: L(μ) - X.
关键词
测度论
广RN性质
向量测度
R-N性质
generalized Radon-Nikodym propety genralized Riesz representative operator shririnking basis
