If $X_n to X_n$ in r-th mean implies $E|X_n^r|to E|X^r|$
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Im reading this article in Wikipedia : https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_mean
In the section Convergence in mean say that if $rgeq 1$ real number and ${X_n}$ a sequence of v.a. souch that $X_n to X$ in r-th mean, this implies $E|X_n^r|to E|X^r|$.
I don't have clear why this result is true and in the wiki there is no explanation.
probability-theory
asked Nov 19 at 19:23
Malena Manzanares
243
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down vote
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Im reading this article in Wikipedia : https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_mean
In the section Convergence in mean say that if $rgeq 1$ real number and ${X_n}$ a sequence of v.a. souch that $X_n to X$ in r-th mean, this implies $E|X_n^r|to E|X^r|$.
I don't have clear why this result is true and in the wiki there is no explanation.
probability-theory
asked Nov 19 at 19:23
Malena Manzanares
243
1
It's a consequence of the reverse triangle inequality for the $L^r$-norm.
– saz
Nov 19 at 19:38
add a comment |
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0
down vote
favorite
up vote
0
down vote
favorite
Im reading this article in Wikipedia : https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_mean
In the section Convergence in mean say that if $rgeq 1$ real number and ${X_n}$ a sequence of v.a. souch that $X_n to X$ in r-th mean, this implies $E|X_n^r|to E|X^r|$.
I don't have clear why this result is true and in the wiki there is no explanation.
probability-theory
asked Nov 19 at 19:23
Malena Manzanares
243
Im reading this article in Wikipedia : https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_mean
In the section Convergence in mean say that if $rgeq 1$ real number and ${X_n}$ a sequence of v.a. souch that $X_n to X$ in r-th mean, this implies $E|X_n^r|to E|X^r|$.
I don't have clear why this result is true and in the wiki there is no explanation.
probability-theory
probability-theory
asked Nov 19 at 19:23
Malena Manzanares
243
asked Nov 19 at 19:23
Malena Manzanares
243
asked Nov 19 at 19:23
Malena Manzanares
243
asked Nov 19 at 19:23
Malena Manzanares
243
asked Nov 19 at 19:23
Malena Manzanares
243
243
1
It's a consequence of the reverse triangle inequality for the $L^r$-norm.
– saz
Nov 19 at 19:38
add a comment |
1
It's a consequence of the reverse triangle inequality for the $L^r$-norm.
– saz
Nov 19 at 19:38
1
1
It's a consequence of the reverse triangle inequality for the $L^r$-norm.
– saz
Nov 19 at 19:38
It's a consequence of the reverse triangle inequality for the $L^r$-norm.
– saz
Nov 19 at 19:38
add a comment |
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It's a consequence of the reverse triangle inequality for the $L^r$-norm.
– saz
Nov 19 at 19:38