The primary problem in property testing is to decide whether a given function satisfies a certain property, or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion is the Hamming distance over the {\em uniform} distribution on the domain. ... more >>>

A function f(x_1, ... , x_d), where each input is an integer from 1 to n and output is a real number, is Lipschitz if changing one of the inputs by 1 changes the output by at most 1. In other words, Lipschitz functions are not very sensitive to small ... more >>>

We study local filters for two properties of functions f:\B^d\to \mathbb{R}: the Lipschitz property and monotonicity. A local filter with additive error a is a randomized algorithm that is given black-box access to a function f and a query point x in the domain of f. Its output is a ... more >>>

A function f : D \to R has Lipschitz constant c if d_R(f(x),f(y)) \leq c\cdot d_D(x,y) for all x,y in D, where d_R and d_D denote the distance functions on the range and domain of f, respectively. We say a function is Lipschitz if it has Lipschitz constant 1. (Note ... more >>>