Hadwiger Integration of Definable Functions

This thesis denes and classies valuations on denable functionals. The intrinsic volumes are valuations on "tame" subsets of R^n, and by easy extension, valuations on functionals on R^n with nitely many level sets, each a "tame" subset of R^n. We extend these valuations, which we call Hadwiger integrals, to denable functionals on R^n, and present some important properties of the valuations. With the appropriate topologies on the set of denable functionals, we obtain dual classication theorems for general valuations on such functionals. We also explore integral transforms, convergence results, and applications of the Hadwiger integrals.

Author dc:creator

• Wright, Matthew

Advisor dc:contributor.advisor

• Robert Ghrist

• Geometry and Topology

Repository record dc:identifier.uri

https://repository.upenn.edu/handle/20.500.14332/49818

OAI identifier oai:identifier

oai:repository.upenn.edu:20.500.14332/49818