A ug 2 00 5 Theory of valuations on manifolds , II .
نویسنده
چکیده
This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which satisfy some additional assumptions. The goal of this article is to introduce a notion of a smooth valuation on an arbitrary smooth manifold and establish some of the basic properties of it.
منابع مشابه
A ug 2 00 6 Theory of valuations on manifolds , IV . New properties of the multiplicative structure
This is the fourth part in the series of articles [4], [5], [6] (see also [3]) where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations is compatible with the product. Then it is proved that the Euler-Verdier involution on smooth valuations is an automorphism of the algebra of valuations. Then an integration functional on valuations wi...
متن کامل2 4 N ov 2 00 5 Theory of valuations on manifolds , II
This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which satisfy some additional assumptions. The goal of this article is to introduce a notion of a smooth valuation on an arbitrary smooth manifold and establish som...
متن کامل1 S ep 2 00 5 Theory of valuations on manifolds , II
This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which satisfy some additional assumptions. The goal of this article is to introduce a notion of a smooth valuation on an arbitrary smooth manifold and establish som...
متن کاملN ov 2 00 5 Theory of valuations on manifolds , IV . New properties of the multiplicative structure
This is the fourth part in the series of articles [4], [5], [6] (see also [3]) where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations is compatible with the product. Then it is proved that the Euler-Verdier involution on smooth valuations is an automorphism of the algebra of valuations. Then an integration functional on valuations wi...
متن کاملA ug 2 00 4 Valuations on convex sets , non - commutative determinants , and pluripotential theory
A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space Hn is presented. In particular new examples of Sp(n)Sp(1)-invariant translation invariant continuous valuations are constructed. This method is based on the theory of plurisubharmonic functions of quaternionic variables developed by the author in two previous papers [5] and [6].
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تاریخ انتشار 2005