Theorem
Let be a function of a set in a measure space and let be a scalar function on . Then is measurable with respect to the σ-algebra generated by in if and only if there exists a measurable function such that, where denotes the Borel set of the real numbers. If only takes finite values, then also only takes finite values.
Read more about this topic: Factorization Lemma
Famous quotes containing the word theorem:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)