Lawrence C. Evans, Ronald F. Garzepy
Abstract
We introduce next certain “lower dimensional” measures on ℝ n which allow us to measure certain “very small” subsets of ℝ n . These are the Hausdorff measures ℋ s , defined in terms of the diameters of various efficient coverings. The idea is that A is an “ s -dimensional subset” of ℝ n if 0 < ℋ s ( A ) < ∞, even if A is very complicated geometrically.
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We introduce next certain “lower dimensional” measures on ℝ n which allow us to measure certain “very small” subsets of ℝ n . These are the Hausdorff measures ℋ s , defined in terms of the diameters of various efficient coverings. The idea is that A is an “ s -dimensional subset” of ℝ n if 0 < ℋ s ( A ) < ∞, even if A is very complicated geometrically.
Key concepts: Hausdorff measure, Measure (data warehouse), Outer measure, Hausdorff space, Mathematics, Computer science, Hausdorff dimension, Pure mathematics