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A New Integral Geometric Formula of the Blaschke‐Petkantschin Type
Author(s) -
Vedel Jensen E. B.,
Kiê 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.19921560105
Subject(s) - mathematics , linear subspace , measure (data warehouse) , blaschke product , hausdorff measure , hausdorff space , product (mathematics) , subspace topology , pure mathematics , type (biology) , mathematical analysis , hausdorff dimension , combinatorics , geometry , ecology , database , computer science , biology
Recently, a new geometric measure decomposition has been derived by Zähle (1990), involving the r ‐fold product of the d ‐dimensional Hausdorff measure with itself. The application to moment measure estimation has been discussed in Jensen et al. (1990a) and Zähle (1990). The decomposition involves, in essence, the rotational invariant measure on r ‐dimensional linear subspaces in R n and the r ‐fold product of the ( d ‐ n + r )‐dimensional Hausdorff measure. In the present paper, we derive another decomposition of this type, involving linear subspaces containing a fixed lower‐dimensional linear subspace. The formula has applications in geometric sampling.