Search results

{{Short description|Annotated index of various modes of convergence}} ...of convergence]]. Simple logical relationships between different modes of convergence are indicated (e.g., if one implies another), formulaically rather than in ...

...[function (mathematics)|function]]s. Like [[absolute convergence|absolute-convergence]], it has the useful property that it is preserved when the order of summat ...ble for series of nonnegative functions, so the notion of uniform absolute-convergence can be used to rule out these possibilities. ...

...<math>(X,\Sigma,\mu)</math> that [[Pointwise convergence#Almost everywhere convergence|converges almost everywhere]] to another integrable function <math>f</math> ...Absolute continuity|absolutely continuous]] [[random variable]]s implies [[convergence in distribution]] of those random variables. ...

...eak convergence coincide. For a general class of spaces, similarly to weak convergence, every bounded sequence has a Delta-convergent subsequence. ...of ''almost convergence,'' by Tadeusz Kuczumow.<ref>T. Kuczumow, An almost convergence and its applications, Ann. Univ. Mariae Curie-Sklodowska Sect. A '''32''' ...

{{Short description|Criterion for convergence of continued fractions}} ...ingsheim theorem''' is a statement about [[Convergent (continued fraction)|convergence]] of certain [[continued fraction]]s. It was discovered by [[Ivan Śleszyńsk ...

In [[mathematical analysis]], '''epi-convergence''' is a type of convergence for [[real-valued function|real-valued]] and [[extended real number line|ex ...or maximization problems. [[Mosco convergence]] is a generalization of epi-convergence to infinite dimensional spaces. ...

...often employed in the study of [[computable analysis]] and [[constructive mathematics]]. ...</math> then <math>\left|x - x_i\right| < \varepsilon</math>. A modulus of convergence is essentially a function that, given <math>\varepsilon</math>, returns a c ...

...ence of sets of random variables]], where convergence is in the sense of [[convergence in probability]].<ref>Dodge, Y. (2003) ''The Oxford Dictionary of Statistic ===Small ''o'': convergence in probability=== ...

...he [[boundary (topology)|boundary]] of its [[radius of convergence|disc of convergence]]. has radius of convergence 1. Then the unit circle is a [[natural boundary]] for the series ''f''. ...

...ences]] or [[limit of a function|functions]] converge to a finite [[limit (mathematics)|limit]] when the argument tends to infinity. ...ences corresponding to sums of many terms, are covered in the article on [[convergence tests]]. ...

{{short description|Convergence of random variables in Banach spaces}} ...nach spaces]]. The theorem shows the equivalence of the different types of convergence for sums of independent and symmetric random variables in Banach spaces. Th ...

...ctions of special form, such as [[polynomial]]s. In more recent work, the convergence of a sequence of operators is studied: these operators generalise the proje ...ow convergence of sequences of linear operators I: almost arbitrarily slow convergence | author1=Frank Deutsch | author2=Hein Hundal | journal=[[Journal of Approx ...

...[mathematical analysis]], a '''general Dirichlet series''' is an [[series (mathematics)|infinite series]] that takes the form of ...ries is convergent at <math>s_0=\sigma_0+t_0i</math>, then it is [[uniform convergence|uniformly convergent]] in the [[Domain of a function|domain]] ...

{{Short description|Variety of proofs provided for the different types of convergence of random variables}} This article is supplemental for “[[Convergence of random variables]]” and provides proofs for selected results. ...

{{short description|Theorem about permutations that preserve convergence for all converging series}} ...infinite [[series (mathematics)|series]] that preserve [[convergent series|convergence]] for all series.<ref>{{cite journal |first=Paul |last=Schaefer |date=1981 ...

{{Short description|Branch of mathematics}} In mathematics, '''chromatic homotopy theory''' is a subfield of [[stable homotopy theory] ...

In the [[mathematics|mathematical branch]] of [[topology]], a '''hyperspace''' (or a space equip * [[Kuratowski convergence]] ...

...ndard notion of convergence of real numbers “→” with one of the types of [[convergence of random variables]]. ...illingsley | first = Patrick | author-link = Patrick Billingsley | title = Convergence of Probability Measures | year = 1969 | publisher = John Wiley & Sons | isb ...

{{Short description|Generalization of the notion of convergence that is found in general topology}} ...ere]] convergence. Many [[topological properties]] have generalizations to convergence spaces. ...

...rgence]] of an [[infinite series]] of [[random variable]]s in terms of the convergence of three different series involving properties of their [[probability distr ...]. The random series <math display="inline">\sum_{n=1}^\infty X_n</math> [[convergence of random variables|converges]] [[almost surely]] in <math>\mathbb{R}</math ...