On Discrete Limits of Sequences of Piecewise Linear Functions

Abstract

In this article we characterize the discrete limits of sequences of piecewise linear functions. A function $f:[0,1]\to \mathbb{R}$ is the discrete limit of a sequence of piecewise linear functions iff there are closed sets $A_n$ such that $[0,1] = \bigcup_nA_n$ and the restricted functions $f/A_n$ are linear.