Hausdorff Measure Through Example

Hausdorff measure is a fundamental tool in geometry and analysis in #Euclidean and metric spaces. We begin by simple examples in the 2D plane and explain the idea.
Our playlist on #Hausdorffmeasure will cover their Definition, Borel regularity, their interaction with Lipchitz and Hölder maps, equality with the Lebesgue measure for integer cases, etc.
#metricspace #fractals #mathematicalanalysis #geometricconstruction #hausdorffmeasure

[@StratosFair]

Super clear explanation ! I was curious because I heard/read in a few places people referring to sets of non-integer Hausdorff dimension and wanted to know what that was about. Everything makes sense now :)

[@YoungMeasures]

Glad to hear.

[@renegirard2173]

Excellent examples that gives the motivation for Hausdorff measure. I am grateful to you for having prepared such a useful video.

[@YoungMeasures]

My pleasure :)

[@renegirard2173]

@@YoungMeasures I would like to add that your video made me understood why the function/mapping H^1_{\delta}{X) increases as \delta -->0. Again very useful video.

[@asmaanaciri9046]

Thank you! That really helps to see the logic behind Hausdorff Measure.

[@YoungMeasures]

Glad that you find it helpful.

[@kz1662]

nicely explained! keep making videos please

[@erwin55226]

Nice Explanation!

[@CosmicConical]

Fantastic video!

[@YoungMeasures]

Glad to hear :)

[@irrationalboi]

Thanks man!
this was useful

[@YoungMeasures]

My pleasue.

[@luisplazabusto9015]

very useful thanks

[@professorno9080]

great video, thank you!