Back Funció mesurable Catalan Měřitelná funkce Czech Messbare Funktion German Mezurebla funkcio Esperanto Función medible Spanish Fonction mesurable French Función medible Galician פונקציה מדידה HE Funzione misurabile Italian 可測関数 Japanese
In mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable. This is in direct analogy to the definition that a continuous function between topological spaces preserves the topological structure: the preimage of any open set is open. In real analysis, measurable functions are used in the definition of the Lebesgue integral. In probability theory, a measurable function on a probability space is known as a random variable.