In measure theory and probability, the monotone class theorem connects monotone classes and 𝜎-algebras. The theorem says that the smallest monotone class containing an algebra of sets is precisely the smallest 𝜎-algebra containing It is used as a type of transfinite induction to prove many other theorems, such as Fubini's theorem.
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probability, the monotoneclasstheorem connects monotoneclasses and 𝜎-algebras. The theorem says that the smallest monotoneclass containing an algebra...
rules and bargaining systems. Monotoneclasstheorem, in measure theory Monotone convergence theorem, in mathematics Monotone polygon, a property of a geometric...
Threshold Logic". IEEE Transactions on Computers. 17 (3). Bernstein's theorem on monotone functions Hausdorff moment problem Monotonic function Cyclical monotonicity...
Monotone comparative statics is a sub-field of comparative statics that focuses on the conditions under which endogenous variables undergo monotone changes...
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...
^{n}(A_{1}\times \cdots \times A_{n})=\prod _{i=1}^{n}\xi (A_{i})} By monotoneclasstheorem, this uniquely defines the product measure on ( S n , B ( S n )...
concept in measure theory, also referred to as an algebra of sets Monotoneclass – theoremPages displaying wikidata descriptions as a fallbackPages displaying...
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization...
Family closed under complements and countable disjoint unions Monotoneclass – theoremPages displaying wikidata descriptions as a fallbackPages displaying...
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....
depending on whether we take monotone or antitone Galois connections). Let (A, ≤) and (B, ≤) be two partially ordered sets. A monotone Galois connection between...
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...
non-empty closed convex sets. The class of firmly nonexpansive operators is equal to the set of resolvents of maximally monotone operators. Surprisingly, while...
volumePages displaying short descriptions of redirect targets Monotoneclass – theoremPages displaying wikidata descriptions as a fallbackPages displaying...
fixed-point of a monotone expression. This augments first-order logic with the ability to express recursion. The Immerman–Vardi theorem, shown independently...
Dirichlet function provides a counterexample showing that the monotone convergence theorem is not true in the context of the Riemann integral. Proof Using...