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Qué (quién) es cyclically monotone function - definición
Totally monotone function; Totally monotone; Totally monotonic; Totally monotonic function; Completely monotone function; Completely monotonic function; Total monotonicity
Monotonic
FUNCTION BETWEEN ORDERED SETS THAT PRESERVES OR REVERSES THE GIVEN ORDER
Montone decreasing; Monotone decreasing; Monotone increasing; Monotonicity; Monotone function; Monotonic; Antitone; Order-preserving; Order-reversing; Monotone map; Increasing function; Decreasing function; Nondecreasing function; Nonincreasing function; Monotone transformation; Monotone operator; Monotonic transformation; Increasing; Strictly increasing; Non-decreasing function; Monotonically decreasing; Monotonically increasing; Monotonically nondecreasing; Monotonically nonincreasing; Monotonic series; Monotonic Function; Strictly decreasing; Order morphism; Decreasing; Monotone sequence; Strictly monotone; Increasing operator; Decreasing operator; Monotonically non-decreasing; Antitonic; Weakly increasing; Weakly decreasing; Strictly increasing function; Monotonicity theorem; Monotone boolean function; Monotonic sequence; Absolute Monotonic Sequence; Absolutely Monotonic Function; Absolutely Monotonic Sequence; Monotonic predicate; Isotone function; Order-preserving function; Antitonicity; Order–preserving function; Order-preserving map; User:Weiße Ziege/sandbox; Monotone function (order theory); Monotone function (topology); Monotonic (function)
·adj ·Alt. of Monotonical.
Decreasing
FUNCTION BETWEEN ORDERED SETS THAT PRESERVES OR REVERSES THE GIVEN ORDER
Montone decreasing; Monotone decreasing; Monotone increasing; Monotonicity; Monotone function; Monotonic; Antitone; Order-preserving; Order-reversing; Monotone map; Increasing function; Decreasing function; Nondecreasing function; Nonincreasing function; Monotone transformation; Monotone operator; Monotonic transformation; Increasing; Strictly increasing; Non-decreasing function; Monotonically decreasing; Monotonically increasing; Monotonically nondecreasing; Monotonically nonincreasing; Monotonic series; Monotonic Function; Strictly decreasing; Order morphism; Decreasing; Monotone sequence; Strictly monotone; Increasing operator; Decreasing operator; Monotonically non-decreasing; Antitonic; Weakly increasing; Weakly decreasing; Strictly increasing function; Monotonicity theorem; Monotone boolean function; Monotonic sequence; Absolute Monotonic Sequence; Absolutely Monotonic Function; Absolutely Monotonic Sequence; Monotonic predicate; Isotone function; Order-preserving function; Antitonicity; Order–preserving function; Order-preserving map; User:Weiße Ziege/sandbox; Monotone function (order theory); Monotone function (topology); Monotonic (function)
·adj Becoming less and less; diminishing.
II. Decreasing ·p.pr. & ·vb.n. of Decrease.
monotonic
FUNCTION BETWEEN ORDERED SETS THAT PRESERVES OR REVERSES THE GIVEN ORDER
Montone decreasing; Monotone decreasing; Monotone increasing; Monotonicity; Monotone function; Monotonic; Antitone; Order-preserving; Order-reversing; Monotone map; Increasing function; Decreasing function; Nondecreasing function; Nonincreasing function; Monotone transformation; Monotone operator; Monotonic transformation; Increasing; Strictly increasing; Non-decreasing function; Monotonically decreasing; Monotonically increasing; Monotonically nondecreasing; Monotonically nonincreasing; Monotonic series; Monotonic Function; Strictly decreasing; Order morphism; Decreasing; Monotone sequence; Strictly monotone; Increasing operator; Decreasing operator; Monotonically non-decreasing; Antitonic; Weakly increasing; Weakly decreasing; Strictly increasing function; Monotonicity theorem; Monotone boolean function; Monotonic sequence; Absolute Monotonic Sequence; Absolutely Monotonic Function; Absolutely Monotonic Sequence; Monotonic predicate; Isotone function; Order-preserving function; Antitonicity; Order–preserving function; Order-preserving map; User:Weiße Ziege/sandbox; Monotone function (order theory); Monotone function (topology); Monotonic (function)
In domain theory, a function f : D -> C is monotonic (or
monotone) if
for all x,y in D, x <= y => f(x) <= f(y).
("<=" is written in LaTeX as sqsubseteq).
(1994-11-24)
Wikipedia
Bernstein's theorem on monotone functions
In real analysis, a branch of mathematics, 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 one important special case the mixture is a weighted average, or expected value.
Total monotonicity (sometimes also complete monotonicity) of a function f means that f is continuous on [0, ∞), infinitely differentiable on (0, ∞), and satisfies
for all nonnegative integers n and for all t > 0. Another convention puts the opposite inequality in the above definition.The "weighted average" statement can be characterized thus: there is a non-negative finite Borel measure on [0, ∞) with cumulative distribution function g such that
the integral being a Riemann–Stieltjes integral.In more abstract language, the theorem characterises Laplace transforms of positive Borel measures on [0, ∞). In this form it is known as the Bernstein–Widder theorem, or Hausdorff–Bernstein–Widder theorem. Felix Hausdorff had earlier characterised completely monotone sequences. These are the sequences occurring in the Hausdorff moment problem.
