EDB — 13P

Exercises

1. [13P]Topics:inf-convolution. Difficulty:*. When $(X,d)$ is a metric space, and $f:X\to ℝ\cup \{+\infty \}$ is l.s.c. and bounded from below, let

   $$f_n(x)\stackrel{.}{=}\underset{y\in X}{inf}\{f(y)+nd(x,y)\}$$

   be the inf-convolution. Show that the sequence $f_n$ is an increasing sequence of Lipschitz functions with $f_n(x){\to }_{n}f(x)$.

   Solution 1

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