Year: 2011
Type: article
Abstract: This thesis defines and classifies valuations on definable functionals. The intrinsic volumes are valuations on "tame" subsets of R^n, and by easy extension, valuations on functionals on R^n with finitely many level sets, each a "tame" subset of R^n. We extend these valuations, which we call Hadwiger integrals, to definable functionals on R^n, and present some important properties of the valuations. With the appropriate topologies on the set of definable functionals, we obtain dual classification theorems for general valuations on such functionals. We also explore integral transforms, convergence results, and applications of the Hadwiger integrals.
Author: Matthew Wright
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: University of Pennsylvania
OpenAlex ID: W1563441957