Errata: Durrett, Exercise 3.6.2

May. 16, 2015

Exercise 3.6.2 of Durrett’s Probability: Theory and Examples, 4th edition is

Show that \(\|\mu-\nu\| \le 2\delta\) if and only if there are random variables \(X\) and \(Y\) with distributions \(\mu\) and \(\nu\) so that \(P(X \ne Y) \le \delta\).

The first inequality should read \(\|\mu-\nu\| \le \delta\).