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. © 2005 Elsevier Inc. All rights reserved.
Alesker, S. (2006). Theory of valuations on manifolds, II. Advances in Mathematics, 207(1), 420–454. https://doi.org/10.1016/j.aim.2005.11.015