8 Concentration of Lipschitz Functions 51 8.1 Concentration on Product Spaces.. .......51 8.2 Concentration of Lipschitz Functions,With a Proof.. ...54 8.3 Martingales,Azuma's Inequality,and Concentration on Permu- tations 8.4 Isoperimetric Inequalities and Concentration on the Sphere...61 9 Concentration:Beyond the Lipschitz Condition 9.1 Talagrand's Inequality·.,,,,·.···.··,,,··,·,64 9.2Theu-Kim Inequality.....··.。..。..········68 8 Concentration of Lipschitz Functions 51 8.1 Concentration on Product Spaces . . . . . . . . . . . . . . . . . . 51 8.2 Concentration of Lipschitz Functions, With a Proof . . . . . . . . 54 8.3 Martingales, Azuma’s Inequality, and Concentration on Permu￾tations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 8.4 Isoperimetric Inequalities and Concentration on the Sphere . . . 61 9 Concentration: Beyond the Lipschitz Condition 64 9.1 Talagrand’s Inequality . . . . . . . . . . . . . . . . . . . . . . . . 64 9.2 The Vu–Kim Inequality . . . . . . . . . . . . . . . . . . . . . . . 68