The Cauchy-Crofton formula and the Whitney arc property for definable\n sets

2008/12/15 by Elisa Vasquez Rifo, Rifo, Elisa Vasquez
Computer Science · Mathematics · #03C64 (Primary) #14P10 (Secondary) #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.0812.2735

openalex publication_date 2008/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the Cauchy-Crofton formula to show that every definable cell (bounded\nby a ball with rational radius) in an O-minimal expansion of a field extension\nof the real numbers satisfies the Whitney arc property.\n

Citations

• The kinematic formula in Riemannian homogeneous spaces

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