This exercise is regarding the measure df defined by the square root of (15.25).

(i) Show that df is not a distance [the definition of a distance is given by the requirements 1–4 below (6.63)].

(ii) Show that df is a stronger measure of descrepancy than the L1-

distance in the sense that p − f

L1 ≤ df (p, f ), where

is the L1-distance between p and f .
(iii) Show that d2 f is a stronger measure of descrepancy than the Kullback–
Leibler information distance defined as

that is, we have dKL(p, f ) ≤ d2 f (p, f ).

Transcribed Image Text:

P ||p - f = \p(x) = f(x)| dx