The Space of Lipschitz Functions is Banach
Problem 11 Chapter 5 of Rudin's Real and Complex Analysis
Changing things up a bit, I'm writing an article on a very theoretical problem. Here, I'll show why the space of all complex functions that satisfy Lipschitz condition of order alpha is a Banach Space for a certain range of alpha.
The proof below is my original thought process and my work
Because it's really convinient to attach a pdf rather than type math here, I'll just add a pdf :D
The problem below is relatively theoretical, but could be read with some theoretical knowledge in abstract measure theory
I hope you enjoyed reading my proof!!!
Credit: Rudin, Walter. Real and Complex Analysis: International Student Edition. McGraw-Hill, 1970.