Mixed measures and functionals of translative integral geometry (Q2718025)
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scientific article; zbMATH DE number 1606243
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mixed measures and functionals of translative integral geometry |
scientific article; zbMATH DE number 1606243 |
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11 April 2002
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integral geometry
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mixed functionals
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mixed measures
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convex bodies
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halfspaces
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spherical integrals
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0.94025135
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0.89488244
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0.8942249
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0.8899344
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0.8859796
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Mixed measures and functionals of translative integral geometry (English)
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The iterated translative versions of classical kinematic integral formulae for intrinsic volumes and curvature measures have led to a series of mixed functionals and mixed measures of convex bodies. Here, the author presents a systematic study of the integral geometric relations which hold for these mixed measures and functionals. Some of the results (the kinematic and Crofton formulae) are generalizations of previously obtained relations but others are new. Among these are formulae for halfspaces, reduction formulae and some representations by spherical integrals (for arbitrary bodies as well as in the centrally symmetric case).
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