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Constancy results for special families of projections

Published online by Cambridge University Press:  07 February 2013

KATRIN FÄSSLER  and
TUOMAS ORPONEN
KATRIN FÄSSLER
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, 00014University of Helsinki, Finland e-mail: [email protected], [email protected]
TUOMAS ORPONEN
Affiliation:
Department of Mathematics and Statistics, University of Helsinki, P.O.B. 68, 00014University of Helsinki, Finland e-mail: [email protected], [email protected]
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Abstract

Let { = V × ℝl : V ∈ G(n−l,m−l)} be the family of m-dimensional subspaces of ℝn containing {0} × ℝl, and let : ℝn → be the orthogonal projection onto . We prove that the mapping V ↦ Dim (B) is almost surely constant for any analytic set B ⊂ ℝn, where Dim denotes either Hausdorff or packing dimension.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 3 , May 2013 , pp. 549 - 568
Copyright
Copyright © Cambridge Philosophical Society 2013

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