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出版Springer-Verlag, 2013-03-08
主題Technology & Engineering / GeneralTechnology & Engineering / Engineering (General)
ISBN33228482489783322848246
URLhttp://books.google.com.hk/books?id=ABCbBgAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋"The authors emphasize the measure-theoretical component of geometry in studying geometric properties of invariant measures under the action of the translation or the motion group. Thereby the representation is concentrated on Hadwiger's convex ring in R d . (The authors are known specialists in this field.) The measure-theoretical approach is chosen twice: first, in form of invariant measures on the transformation groups or on sets of affine subspaces (Chapter I) and, secondly, by invariant geometric measures for the convex bodies and their finite unions (Chapter II). The latter means that the classical quermassintegrals are refined to Federer's curvature measures which leads to local as well as global results. Chapters III and IV contain the most important formulas of integral geometry on the convex ring such as the principal kinematic formula (and its translative version due to the authors), Crofton's formula, projection formulas and others. Applications to mean value relations in stochastic geometry may be found in Chapter V. Finally, in Chapter VI integral-geometric formulas of the Blaschke- Petkantschin-type are treated which are related to higher-order moment measures in stochastic geometry."--Website