### Quick description

You are given a (bad) continuous real function on a compact metric space ; suppose you have a tool that applies well for Lipschitz functions, with good monotonicity properties; Then compare with Lipschitz dominators: For let . Then is the minimum Lipschitz dominator for with Lipschitz constant .

### General discussion

This is a lot like convolution with an approximate delta function; making the translations

## Comments

## This looks nice, but do you

Thu, 11/06/2009 - 09:57 — Anonymous (not verified)This looks nice, but do you plan to give some examples of problems where this trick is useful? It would be a big help.

## useful!?

Thu, 11/06/2009 - 18:50 — mckeown_j.cOh yes... "tricks" wiki... yeah, it came up in a complex/harmonic analysis course I was taking, but the context... remains elusive.

## Closely related is P

Sat, 13/06/2009 - 16:23 — mckeown_j.cClosely related is Péron's expression solving the harmonic Dirichlet problem, as an infimum of sup-harmonic dominators.