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Absolute curvature measures for unions of sets with positive reach
Author(s) -
Rataj Jan
Publication year - 2002
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300016028
Subject(s) - mathematics , absolute (philosophy) , curvature , intersection (aeronautics) , function (biology) , measure (data warehouse) , index (typography) , mathematical analysis , geometry , philosophy , epistemology , database , evolutionary biology , world wide web , computer science , engineering , biology , aerospace engineering
Absolute curvature measures for locally finite unions of sets with positive reach are introduced, extending the definition of Zähle [13] by taking into account the absolute value of the index function. It is shown that this definition differs from that of Matheron [5] and Schneider [12]. An intersection formula of Crofton type for absolute curvature measures is proved. The role of absolute curvature measures in geometric statistics is illustrated by an example.