Difference between revisions of "Talk:Rectifiable set"
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'''Definition 2''': is it clear what is meant by "$k$-dimensional graphs of $\mathbb R^n$"? --[[User:Boris Tsirelson|Boris Tsirelson]] 09:43, 4 August 2012 (CEST) | '''Definition 2''': is it clear what is meant by "$k$-dimensional graphs of $\mathbb R^n$"? --[[User:Boris Tsirelson|Boris Tsirelson]] 09:43, 4 August 2012 (CEST) | ||
| − | As far as I remember, Hausdorff dimension ''k'' does not imply finite (or even σ-finite) ''k''-dimensional Hausdorff measure. Really so? And then "might not be $\mathcal{H}^k$-measurable" looks strange. Is it OK? --[[User:Boris Tsirelson|Boris Tsirelson]] 09:50, 4 August 2012 (CEST) | + | As far as I remember, Hausdorff dimension ''k'' does not imply finite (or even σ-finite) ''k''-dimensional Hausdorff measure. Really so? And then "might not be $\mathcal{H}^k$-measurable" looks strange. Is it OK? Do the definitions implicit here conform to definitions in [[Hausdorff measure]] and [[Hausdorff dimension]]? --[[User:Boris Tsirelson|Boris Tsirelson]] 09:50, 4 August 2012 (CEST) |
Revision as of 07:53, 4 August 2012
Definition 2: is it clear what is meant by "$k$-dimensional graphs of $\mathbb R^n$"? --Boris Tsirelson 09:43, 4 August 2012 (CEST)
As far as I remember, Hausdorff dimension k does not imply finite (or even σ-finite) k-dimensional Hausdorff measure. Really so? And then "might not be $\mathcal{H}^k$-measurable" looks strange. Is it OK? Do the definitions implicit here conform to definitions in Hausdorff measure and Hausdorff dimension? --Boris Tsirelson 09:50, 4 August 2012 (CEST)
How to Cite This Entry:
Rectifiable set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rectifiable_set&oldid=27352
Rectifiable set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rectifiable_set&oldid=27352