Tricki

## To make a function less variable without changing it much, compare it with less variable functions

 This article is a stub.This means that it cannot be considered to contain or lead to any mathematically interesting information.

### 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

indicates that we've replaced the ring of real numbers with the tropical rig, for which behaves a lot like the delta-function approximation .

### This looks nice, but do you

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!?

Oh 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

Closely related is Péron's expression solving the harmonic Dirichlet problem, as an infimum of sup-harmonic dominators.