An -net is any of several related concepts in mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, and has a particular meaning in probability theory

Probability theory

Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...

 where it is used in desription of the approximation of one probability distribution by another.

Theory

Let be a probability distribution

Probability distribution

In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

over some set . An -net for a class of subsets of is any subset such that
for any


Intuitively approximates the probability distribution.

A stronger notion is -approximation. An -approximation for class is a subset such that for any it holds