probability, the monotone class theorem connects monotone classes and 𝜎-algebras. The theorem says that the smallest monotone class containing an algebra...

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

theory) Maharam's theorem (measure theory) Minlos's theorem (functional analysis) Monotone class theorem (measure theory) Prokhorov's theorem (measure theory)...

the Carathéodory extension theorem for 𝜎-finite measures. The π-𝜆 theorem is closely related to the monotone class theorem, which provides a similar...

converse is true as well, by Dynkin's theorem (see below). This theorem (or the related monotone class theorem) is an essential tool for proving many...

restriction of an entire function to the real line. Bernstein's theorem on monotone functions: A function f ( x ) {\displaystyle f(x)} that is absolutely...

form m2i. Therefore, by Dilworth's theorem, the width of this partial order is n. The Erdős–Szekeres theorem on monotone subsequences can be interpreted...

fact, for these two variants of SAT, Schaefer's dichotomy theorem shows that their monotone versions (where negations of variables are not allowed) are...

D.; Cohen, Arthur; Strawderman, W.E. (1976). "A complete class theorem for strict monotone likelihood ratio with applications". Annals of Statistics...

Versions of the theorem have been proved for different types of preferences, with different classes of exceptions. A version of the theorem was first proved...

^{n}(A_{1}\times \cdots \times A_{n})=\prod _{i=1}^{n}\xi (A_{i})} By monotone class theorem, this uniquely defines the product measure on ( S n , B ( S n )...

languages). The hierarchy theorems are used to demonstrate that the time and space complexity classes form a hierarchy where classes with tighter bounds contain...

result from this area is the unique factorization theorem. There is no consensus for the meaning of "monotone property" in graph theory. Examples of definitions...

and operator monotone, while f ( t ) = t log ⁡ ( t ) {\displaystyle f(t)=t\log(t)} is operator convex. The original proof of this theorem is due to K....

complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the class of such problems is called NPI. Ladner's theorem, shown...

Monotone comparative statics is a sub-field of comparative statics that focuses on the conditions under which endogenous variables undergo monotone changes...

in the monotone case, i.e., when there are no negations (#MONOTONE-2-CNF). It is known that, assuming that NP is different from RP, #MONOTONE-2-CNF also...

depending on whether we take monotone or antitone Galois connections). Let (A, ≤) and (B, ≤) be two partially ordered sets. A monotone Galois connection between...

non-empty closed convex sets. The class of firmly nonexpansive operators is equal to the set of resolvents of maximally monotone operators. Surprisingly, while...

does not vanish – the Whitney–Graustein theorem classified these by turning number by considering the homotopy class of the Gauss map and showing that this...

In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization...

all of them are completely monotone, i.e. d-monotone for all   d ∈ N   {\displaystyle \ d\in \mathbb {N} \ } or d-monotone for certain   θ ∈ Θ   {\displaystyle...

fixed-point of a monotone expression. This augments first-order logic with the ability to express recursion. The Immerman–Vardi theorem, shown independently...

statistic which is not complete. This is important because the Lehmann–Scheffé theorem cannot be applied to such models. Galili and Meilijson 2016 propose the...

shown to be true for vertex guards in two special sub-classes of simple polygons, viz. monotone polygons and polygons weakly visible from an edge. Krohn...

adjoint and g is called the upper adjoint. By the adjoint functor theorem, a monotone map between any pair of preorders preserves all joins if and only...

course at the United States Marine Corps School of Infantry Monotone convergence theorem, in mathematics Motivation crowding theory, in economics Member...

t\rightarrow P_{t}f(x)} is right continuous. Therefore, together with the monotone class theorem, for any universally measurable function f {\displaystyle f} , the...

{\displaystyle \int _{0}^{\infty }g(t)\,dt<\infty } g is monotone and non-increasing The key renewal theorem states that, as t → ∞ {\displaystyle t\rightarrow...

Dirichlet function provides a counterexample showing that the monotone convergence theorem is not true in the context of the Riemann integral. Proof Using...