# 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 $$\|\mu-\nu\| \le \delta$$.