Bartle’s proof of the Riesz-Fischer theorem ( spaces are complete) is quite nice. Royden uses a concept called “rapidly Cauchy”, which may complicated things unnecessarily.
Proof from Bartle’s Book Elements of Integration:
Bartle’s proof of the Riesz-Fischer theorem ( spaces are complete) is quite nice. Royden uses a concept called “rapidly Cauchy”, which may complicated things unnecessarily.
Proof from Bartle’s Book Elements of Integration: