# unconditional convergence

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unconditional convergence
1. the property of a convergent infinite series that remains convergent when the terms are arranged in any order.

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Universalium. 2010.

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• Unconditional convergence — In mathematical analysis, a series sum {n=1}^infty x n in a Banach space X is unconditionally convergent if for every permutation sigma: mathbb N o mathbb N the series sum {n=1}^inftyx {sigma(n)} converges.This notion is often defined in an… …   Wikipedia

• unconditional convergence — Math. 1. the property of a convergent infinite series that remains convergent when the terms are arranged in any order. 2. See absolute convergence …   Useful english dictionary

• Modes of convergence (annotated index) — The purpose of this article is to serve as an annotated index of various modes of convergence and their logical relationships. For an expository article, see Modes of convergence. Simple logical relationships between different modes of… …   Wikipedia

• Absolute convergence — In mathematics, a series (or sometimes also an integral) of numbers is said to converge absolutely if the sum (or integral) of the absolute value of the summand or integrand is finite. More precisely, a real or complex series is said to converge… …   Wikipedia

• Modes of convergence — In mathematics, there are many senses in which a sequence or a series is said to be convergent. This article describes various modes (senses or species) of convergence in the settings where they are defined. For a list of modes of convergence,… …   Wikipedia

• absolute convergence — noun : convergence of a mathematical series when the absolute values of the terms are taken * * * Math. 1. the property of an infinite series in which the series formed by replacing each term in the original series with its absolute value… …   Useful english dictionary

• Conditional convergence — In mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely. Definition More precisely, a series is said to converge conditionally if exists and is a finite number (not ∞ or −∞) …   Wikipedia

• absolute convergence — Math. 1. the property of an infinite series in which the series formed by replacing each term in the original series with its absolute value converges. Cf. conditional convergence. 2. the property of a sequence of functions in which the series… …   Universalium

• Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely. In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

• Unbedingte Konvergenz — Die unbedingte Konvergenz ist ein Begriff aus der Funktionalanalysis, der ein bestimmten Konvergenzverhalten von Reihen beschreibt. Man spricht von unbedingter Konvergenz einer Reihe, wenn die Konvergenz unempfindlich gegenüber Umordnungen der… …   Deutsch Wikipedia