whereF denotes the complement of event F and 1 F and 1F denote indicator functions for F andF , respectively.
when F happens, we can replace Z c by Z with a 1 ± z factor loss: The first term of the RHS of (A.2) equals to we can use E [1F ] = Pr[F ] ≤ exp(−Ω(log 2 n)) to show that the second term of RHS of (A.2) is negligible, This claim must be handled somewhat carefully since the RHS does not depend on d at all.