Wikipedia

User:IntegralPython/sandbox/Fractal measure: Difference between revisions

Browse history interactively
← Previous editNext edit →
Content deleted Content added
VisualWikitext
The measure I was describing is indeed different to Hausdorff measure and apparently also to the "Spherical measure" page. It is, however, important as it is much easier to construct than the Hausdorff measure.
rm untrue info
Line 19:
 
<math>H^s(E) \le S^s(E) \le 2H^s(E)</math>.<ref name="Geometric Outer-Measures"/> {{clarify|reason=Covering by balls gives a different result than covering by general shapes; how this works needs to be explained in detail.}}
 
This construction is how the Hausdorff and [[packing measure]]s are obtained.{{clarify|reason=This statement is incorrect, the packing measure is NOT obtained in this way. In the above, you are covering the set to be measured, by contrast, the packing measure doe NOT cover, it jams balls into the inside, and only then uses the cartheodory extension theorem to get a measure. Don't confuse the covering used in the extension with the covering of the set itself...}}
 
==Hausdorff measure==
Retrieved from "https://en.wikipedia.org/wiki/User:IntegralPython/sandbox/Fractal_measure"