almost surely

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• Almost surely — In probability theory, one says that an event happens almost surely (a.s.) if it happens with probability one. The concept is analogous to the concept of almost everywhere in measure theory. It is often encountered in questions that involve… …   Wikipedia

• Almost Mathieu operator — In mathematical physics, the almost Mathieu operator arises in the study of the quantum Hall effect. It is given by: [H^{lambda,alpha} omega u] (n) = u(n+1) + u(n 1) + 2 lambda cos(2pi (omega + nalpha)) u(n), , acting as a self adjoint operator… …   Wikipedia

• Almost all — In mathematics, the phrase almost all has a number of specialised uses. Almost all is sometimes used synonymously with all but finitely many (formally, a cofinite set) or all but a countable set (formally, a cocountable set); see almost. An… …   Wikipedia

• Almost everywhere — In measure theory (a branch of mathematical analysis), one says that a property holds almost everywhere if the set of elements for which the property does not hold is a null set, i.e. is a set with measure zero, or in cases where the measure is… …   Wikipedia

• Almost — In mathematics, especially in set theory, when dealing with sets of infinite size, the term almost or nearly is used to mean all the elements except for finitely many . In other words, an infinite set S that is a subset of another infinite set L …   Wikipedia

• Convergence of random variables — In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to …   Wikipedia

• pre-Columbian civilizations — Introduction       the aboriginal American Indian (Mesoamerican Indian) cultures that evolved in Meso America (part of Mexico and Central America) and the Andean region (western South America) prior to Spanish exploration and conquest in the 16th …   Universalium

• Europe, history of — Introduction       history of European peoples and cultures from prehistoric times to the present. Europe is a more ambiguous term than most geographic expressions. Its etymology is doubtful, as is the physical extent of the area it designates.… …   Universalium

• Infinite monkey theorem — Not to be confused with Hundredth monkey effect. Given enough time, a hypothetical monkey typing at random would, as part of its output, almost surely produce all of Shakespeare s plays. In this image a chimpanzee is giving it a try. The infinite …   Wikipedia

• Fatou's lemma — In mathematics, Fatou s lemma establishes an inequality relating the integral (in the sense of Lebesgue) of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after the French… …   Wikipedia

• Erdős–Rényi model — In graph theory, the Erdős Rényi model, named for Paul Erdős and Alfréd Rényi, is either of two models for generating random graphs, including one that sets an edge between each pair of nodes with equal probability, independently of the other… …   Wikipedia