Calculations of Hausdorff dimension can be quite difficult via direct computation, so instead most of the time estimating Hausdorff dimension is good enough! We'll look at the definition of Hausdorff dimension again to see why it is hard to calculate directly, go through a method for estimating Hausdorff Dimension that gives upperbounds through some combinatorial geometry regarding finite covers of a certain maximum radius, and then lastly go through an argument for The Mass Distribution Principle a fairly well known method for finding lower bounds.
0:00 Intro
0:10 Why is it "hard" to calculate Hausdorff Dimension?
0:45 Estimating Hausdorff Dimension: a method for finding upperbounds
4:07 Estimating Hausdorff Dimension: The Mass Distribution Principle for lower bounds
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4 июл 2024
