EDB β€” 13P

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Exercises

  1. [13P]Topics:inf-convolution. Difficulty:*. When (X,d) is a metric space, and f:X→ℝβˆͺ{+∞} is l.s.c. and bounded from below, let

    fn(x)=.infy∈X{f(y)+nd(x,y)}

    be the inf-convolution. Show that the sequence fn is an increasing sequence of Lipschitz functions with fn(x)β†’nf(x).

    Solution 1

    [13Q]

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  • inf-convolution
  • metric space
  • lower semicontinuous
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