Hausdorff dimension and non-degenerate families of projections

Details Hausdorff dimension and non-degenerate families of projections Hausdorff dimension and non-degenerate families of projections

2012-03-23

arxiv.org/abs/1203.5296v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We study parametrized families of orthogonal projections for which the dimension of the parameter space is strictly less than that of the Grassmann manifold. We answer the natural question of how much the Hausdorff dimension may decrease by verifying the best possible lower bound for the dimension of almost all projections of a finite measure. We also show that a similar result is valid for smooth families of maps from $n$-dimensional Euclidean space to $m$-dimensional one.

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