A function f:X->R is measurable if, for every real number a, the set {x element X:f(x)>a} is measurable. When X = R with Lebesgue measure, or more generally any Borel measure, then all continuous functions are measurable. In fact, practically any function that can be described is measurable. Measurable functions are closed under addition and multiplication, but not composition.

Borel measure | Lebesgue measure | measure | measure space | measure theory | real function | sigma-algebra