Geometric Measure Theory prerequisites

Question

What are topics good to familiarize oneself with, if one wants to study geometric measure theory?

I've learned exterior algebra (Grassmann algebra), and I want to know if I should seek anything next, or just jump into textbooks on Geometric Measure Theory. Maybe differential geometry?

Answer 1

I recommend the classical book of Federer (Herbert Federer. Geometric measure theory. 1969). It has the opinion of being hard to digest but I believe it is a matter of methodology (and taste). It is also really self-contained so you do not need know much beforehand (apart from some point-set topology). My advice is the following:

1. read from the first chapter without omitting anything and make notes;
2. be prepared to invest 2-3 working months (not doing anything else) to get acquainted with the topic;
3. teach someone what you have learned.

I think it is not really possible to "jump into" the topic.