Bourgain’s discretization theorem
Bourgain’s discretization theorem asserts that there exists a universal constant with the following property. Let be Banach spaces with . Fix and set . Assume that is a -net in the unit ball of and that admits a bi-Lipschitz embedding into with distortion at most . Then the entire space admits a bi-Lipschitz embedding into with distortion at most . This mostly expository article is devoted to a detailed presentation of a proof of Bourgain’s theorem.We also obtain an improvement...