In Week 5 of my Geometric Measure Theory course, we’ll be studying Lipschitz functions and various useful techniques for working with them. In this note I’m going to discuss one of my favorite results from this week and show how I illustrated it using Numpy and Matplotlib. Neither the theorem nor the code are difficult, but I’ve always wanted to visualize this theorem, and coding it is a nice exercise.
In Week 3 of the Geometric Measure Theory course I’m teaching, an important class of objects we discuss are Frostman measures. An s-Frostman Measure is a measure $ \mu$ in Euclidean space so that $ \mu(B(x,r))\leq Cr^s$ for any ball $ B(x,r)$. In this note I show how I generated illustrations of them using Matplotlib.