[13P]Topics:inf-convolution. Difficulty:*. When (X,d) is a metric space, and f:Xβββͺ{+β} is l.s.c. and bounded from below, let
be the inf-convolution. Show that the sequence fn is an increasing sequence of Lipschitz functions with fn(x)βnf(x).
[13Q]βΊβ»