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We extend the classical Crofton formulas in Euclidean integral geometry to Finsler metrics on $\R^n$ whose geodesics are straight lines.

Copyright 1998 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 04 (1998), pp. 91-100
• Publisher Identifier: S 1079-6762(98)00053-5
• 1991 Mathematics Subject Classification. Primary 53C65
• Key words and phrases.Crofton formulas, Hilbert's fourth problem, Finsler geometry
• Received by the editors August 08, 1998
• Posted on November 23, 1998
• Communicated by Dmitri Burago
• Comments (When Available)

J. C. Alvarez Paiva

Universite Catholique de Louvain, Institut de Mathematique Pure et Appl., Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium

E-mail address: alvarez@agel.ucl.ac.be

E. Fernandes

Universite Catholique de Louvain, Institut de Mathematique Pure et Appl., Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium

E-mail address: fernandes@agel.ucl.ac.be