One way of interpreting the convergence of a sequence Xn to X is to say that the ''distance'' between X and Xn is getting smaller and smaller.

Furthermore, if r > s ≥ 1, convergence in r-th mean implies convergence in s-th mean. Hence, convergence in mean square implies convergence in mean. Convergence of measures · Proofs · Fatou's lemma · Borel–Cantelli lemma

The phrase "convergence in mean" is used in several branches of mathematics to refer to a number of different types of sequential convergence.

A sequence of random vectors is convergent in mean-square if and only if all the sequences of entries of the random vectors are. Proposition ...

8 апр. 2015 г. · having the limit A A , then also the sequence (2) converges to the limit A A . Thus, a convergent sequence is always convergent in the mean.

Although the definition of converge in mean square encompasses conver- gence to a random variable, in many applications we shall encounter con- vergence to a ...

the fact that two or more things, ideas, etc. become similar or come together: a convergence of interests/opinions/ideas.

7 мар. 2014 г. · Show that Var[Xn]→Var[X]. Convergence in mean square implies that as n→∞ we have that E[(Xn−X)2]→0. proof that convergence in mean implies ... - Math Stack Exchange Does convergence of means imply convergence in mean? Does convergence in probability implies convergence of the ... Convergence in mean square implies convergence in mean Другие результаты с сайта math.stackexchange.com

The meaning of CONVERGENCE is the act of converging and especially moving toward union or uniformity; especially : coordinated movement of the two eyes so ...

Some derived cases for the convergence in rth mean are convergence in mean, obtained by putting r = 1 and convergence in mean square obtained by putting r = 2.