Bernstein's theorem states that every real-valued function on the half-line [0, ∞) that is totally monotone is a mixture of exponential functions. In...

Bernstein inequalities in probability theory Bernstein polynomial Bernstein's problem Bernstein's theorem (approximation theory) Bernstein's theorem on...

Bernstein's theorem on monotone functions Bernstein's theorem (approximation theory) Bernstein's theorem (polynomials) Bernstein's lethargy theorem Bernstein–von...

of absolutely monotonic functions derive from theorems. Bernstein's little theorem: A function that is absolutely monotonic on a closed interval [ a ,...

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...

consequence of Bernstein's theorem on monotone functions applied to the integral representation coming from Binet's first integral for the gamma function. Additionally...

Differentiable function Integrable function Square-integrable function, p-integrable function Monotonic function Bernstein's theorem on monotone functions – states...

Bernstein's theorem on monotone functions Continuous-repayment mortgage Hamburger moment problem Hardy–Littlewood Tauberian theorem Laplace–Carson transform...

equations. Let us restate the theorem. For a complete lattice ⟨ L , ≤ ⟩ {\displaystyle \langle L,\leq \rangle } and a monotone function f : L → L {\displaystyle...

In linear algebra, the operator monotone function is an important type of real-valued function, fully classified by Charles Löwner in 1934. It is closely...

functions with respect to the size or depth of circuits that can compute them. A Boolean function may be decomposed using Boole's expansion theorem in...

problems Sergey Bernstein, developed the Bernstein polynomial, Bernstein's theorem on monotone functions and Bernstein inequalities in probability theory Nikolay...

number of density functions tends to the normal density as the number of density functions increases without bound. These theorems require stronger hypotheses...

zeta function. This expresses the polygamma function as the Laplace transform of ⁠(−1)m+1 tm/1 − e−t⁠. It follows from Bernstein's theorem on monotone functions...

Trombi–Varadarajan theorem (Lie group) Anderson's theorem (real analysis) Bernstein's theorem (functional analysis) Bohr–Mollerup theorem (gamma function) Bolzano's...

theory, Bernstein polynomial, Bernstein's problem, Bernstein's theorem, Bernstein's theorem on monotone functions, Bernstein–von Mises theorem Yogi Berra...

likelihood function is of the utmost importance. By the extreme value theorem, it suffices that the likelihood function is continuous on a compact parameter...

appropriate functions between them. A simple example of an order theoretic property for functions comes from analysis where monotone functions are frequently...

output changing from 1 to 0. Operations with this property are said to be monotone. Thus the axioms thus far have all been for monotonic Boolean logic. Nonmonotonicity...

function" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem:...

example of a monotone function is the following function on the cycle with 6 elements: f(0) = f(1) = 4, f(2) = f(3) = 0, f(4) = f(5) = 1. A function is called...

field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered...

case. An example is the Knaster–Tarski theorem, which states that the set of fixed points of a monotone function on a complete lattice is again a complete...

algebra (logic) Boolean algebra topics Boolean domain Boolean function Boolean-valued function Conjunction/disjunction duality Disjunctive syllogism Fréchet...

negation is intuitionistically provable. This result is known as Glivenko's theorem. De Morgan's laws provide a way of distributing negation over disjunction...

upper bound. Closure operator. A closure operator on the poset P is a function C : P → P that is monotone, idempotent, and satisfies C(x) ≥ x for all x in...

now known as the von Neumann–Morgenstern utility theorem; many similar utility representation theorems exist in other contexts. In 1738, Daniel Bernoulli...

with lower BIC are generally preferred. It is based, in part, on the likelihood function and it is closely related to the Akaike information criterion...

a branch of mathematics, an order embedding is a special kind of monotone function, which provides a way to include one partially ordered set into another...

and (open) continuous maps, and the category of preorders and (bounded) monotone maps, providing the preorder characterizations as well as the interior...