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A Coarea Formula for Multiple Geometric Integrals
Author(s) -
Kiêu K.
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921560106
Subject(s) - mathematics , simple (philosophy) , hausdorff space , transformation (genetics) , product (mathematics) , pure mathematics , mathematical analysis , geometry , philosophy , biochemistry , chemistry , epistemology , gene
The coarea formula by Federer (1969) is a general transformation formula for simple geometric integrals. In the present paper, we derive a coarea formula for multiple geometric integrals. The construction of this new formula is based on the use of the simple coarea formula on a product of Hausdorff rectifiable sets. Also, this coarea formula for multiple integrals is extended, so it can be applied to the locally Hausdorff rectifiable sets described in Zähle (1982). An application of the formula resulting in new Blaschke‐Petkantschin formulae is presented in Jensen and Kiêu (1991).