# Lebesgue number

### From Conservapedia

The **Lebesgue number** of an open cover *C* of a metric space *(X, d)* is a real number δ > 0 such that if a subset *A* of *X* has diameter less than δ, then *A* is contained in at least one element of *C*. If *X* is compact, then it has at least one Lebesgue number.