What is Hausdorff Dimension? Intuition, Gauge Functions, and Hausdorff Measures

A stab at one of the introductory questions in fractal geometry "What is Hausdorff Dimension?", this video starts intuitively with an analysts notion of dimension form the perspective of scaling before introducing gauge functions, Hausdorff outer measures and Hausdorff measures. With these measures defined we look at an important family of gauge functions to define the Hausdorff dimension, that which captures the intuition described at the beginning of the video. In fractal geometry Hausdorff dimension is a pretty fundamental concept so I hope you learn a bit about it here!

00:00 Wholesome Nathan Content
00:24 Intuition for Hausdorff Dimension
05:58 What is a gauge funciton?
07:23 What are Hausdorff Measures?
10:50 What is Hausdorff Dimension?

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