A Hausdorff Measure Inequality

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1976Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 219, page 361 (issn: 0002-9947,

Copyright policy )

Authors: Ernst, Lawrence R.; Freilich, Gerald;

doi: 10.2307/1997601 , 10.1090/s0002-9947-1976-0419739-8

A Hausdorff Measure Inequality

- Summary
- Subjects
- Metrics

Abstract

We prove that the Hausdorff ( m + k ) (m + k) -measure of a product set is no less than the product of the Hausdorff m-measure of the (measurable) first component set in R m {{\mathbf {R}}^m} and the (finite) Hausdorff k-measure of the second component in R n {{\mathbf {R}}^n} .

Keywords

Length, area, volume, other geometric measure theory, Measures and integrals in product spaces

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	4
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average