field of real analysis, the monotone convergence theorem is any of a number of related theorems proving the good convergence behaviour of monotonic sequences...

martingale convergence theorem is a random variable analogue of the monotone convergence theorem, which states that any bounded monotone sequence converges. There...

rules and bargaining systems. Monotone class theorem, in measure theory Monotone convergence theorem, in mathematics Monotone polygon, a property of a geometric...

sufficient condition for the convergence of expected values of random variables. Lebesgue's dominated convergence theorem. Let ( f n ) {\displaystyle (f_{n})}...

there exists a monotone subsequence, likewise also bounded. It follows from the monotone convergence theorem that this subsequence converges. The general...

f dμ ≤ dν. The supremum of all such functions, along with the monotone convergence theorem, then furnishes the Radon–Nikodym derivative. The fact that the...

mathematics, the integral test for convergence is a method used to test infinite series of monotonic terms for convergence. It was developed by Colin Maclaurin...

(following from Brouwer's bar theorem) and is strong enough to give short proofs of key theorems. The monotone convergence theorem (described as the fundamental...

on N {\displaystyle N} . Fatou's lemma does not require the monotone convergence theorem, but the latter can be used to provide a quick and natural proof...

take limits under the integral sign (via the monotone convergence theorem and dominated convergence theorem). While the Riemann integral considers the area...