TY - JOUR

T1 - Packing dimensions of projections and dimension profiles

AU - Falconer, Kenneth John

AU - Howroyd, JD

N1 - Howroyd was a research assistant of Falconer at the time of writing.

PY - 1997/3

Y1 - 1997/3

N2 - For E a subset of R(n) and 0 less than or equal to m less than or equal to n we define a 'family of dimensions' Dim(m)E, closely related to the packing dimension off, with the property that the orthogonal projection of E onto almost all m-dimensional subspaces has packing dimension Dim(m)E. In particular the packing dimension of almost all such projections must be equal. We obtain similar results for the packing dimension of the projections of measures. We are led to think of Dim(m)E for m is an element of [0, n] as a 'dimension profile' that reflects a variety of geometrical properties of E, and we characterize the dimension profiles that are obtainable in this way.

AB - For E a subset of R(n) and 0 less than or equal to m less than or equal to n we define a 'family of dimensions' Dim(m)E, closely related to the packing dimension off, with the property that the orthogonal projection of E onto almost all m-dimensional subspaces has packing dimension Dim(m)E. In particular the packing dimension of almost all such projections must be equal. We obtain similar results for the packing dimension of the projections of measures. We are led to think of Dim(m)E for m is an element of [0, n] as a 'dimension profile' that reflects a variety of geometrical properties of E, and we characterize the dimension profiles that are obtainable in this way.

KW - SETS

UR - http://www.scopus.com/inward/record.url?scp=21444454260&partnerID=8YFLogxK

M3 - Article

SN - 0305-0041

VL - 121

SP - 269

EP - 286

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

ER -