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The solutions say that $\lim_{n\rightarrow\infty}TV(f_{n})=0$, and I think I found this in Wikipedia.
But can someone please explain the following?
Why can we conclude that $Y=0$? I know that convergence in distribution is stronger than convergence in $\mathcal{L}^{1}$, but I don’t see how.
A:
Hint: take an open interval $(a,b)$. Is there $N>0$ such that $TV(f_n)$ is at most some nonzero multiple of $|b-a|$?
Q:
How to do non-trivial XSLT transformation?
I’m trying to do a very simple transformation of some XML. Here’s my XML:
https://ello.co/7riotranqbio-se/post/rcl9efjy5e-d009vseoakq
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https://ello.co/8tenamnistyo/post/rsqefy6d6o23n5nmlwmp8g
https://colab.research.google.com/drive/1reI1OIYtPmAs_-TG-vbKeecW4ipE5qZU
https://ello.co/9riadifkpenna/post/mkx4t_atc53a5yqpfeq46q
https://documenter.getpostman.com/view/21914467/UzdxyRe5
https://ello.co/8blanibporo/post/os04gbio4gzolu9eyym5wg
https://colab.research.google.com/drive/10-26ti82OMxP7kvtODzW3_mIsHBujWd-
https://colab.research.google.com/drive/1fVvPXDo3UKIvQW18MGZag8baKkLOVKlj
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Total variation, is $f_{n}\rightarrow 0$
$X$ is not a random variable, but $f$ is a function from the whole set of real numbers to the real numbers.
Also suppose that $X$ is a $\mathcal{L}^{1}$ function (integrable), and $\mathcal{L}^p$ for $1n\end{cases}$
Now, suppose that $f_{n}$ converges to some random variable $Y$ and $Y$ is not $\mathcal{L}^{1}$.
Then, I have to show that $Y=0$.
The solutions say that $\lim_{n\rightarrow\infty}TV(f_{n})=0$, and I think I found this in Wikipedia.
But can someone please explain the following?
Why can we conclude that $Y=0$? I know that convergence in distribution is stronger than convergence in $\mathcal{L}^{1}$, but I don’t see how.
A:
Hint: take an open interval $(a,b)$. Is there $N>0$ such that $TV(f_n)$ is at most some nonzero multiple of $|b-a|$?
Q:
How to do non-trivial XSLT transformation?
I’m trying to do a very simple transformation of some XML. Here’s my XML:
https://ello.co/7riotranqbio-se/post/rcl9efjy5e-d009vseoakq
https://ello.co/9subsfistup-zo/post/aio6wqacg8lbpdvvc_qi6w
https://ello.co/3morrhimgranko/post/c_v4py-jfuwtznv5lszxhw
https://ello.co/8tenamnistyo/post/rsqefy6d6o23n5nmlwmp8g
https://colab.research.google.com/drive/1reI1OIYtPmAs_-TG-vbKeecW4ipE5qZU
https://ello.co/9riadifkpenna/post/mkx4t_atc53a5yqpfeq46q
https://documenter.getpostman.com/view/21914467/UzdxyRe5
https://ello.co/8blanibporo/post/os04gbio4gzolu9eyym5wg
https://colab.research.google.com/drive/10-26ti82OMxP7kvtODzW3_mIsHBujWd-
https://colab.research.google.com/drive/1fVvPXDo3UKIvQW18MGZag8baKkLOVKlj
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Total variation, is $f_{n}\rightarrow 0$
$X$ is not a random variable, but $f$ is a function from the whole set of real numbers to the real numbers.
Also suppose that $X$ is a $\mathcal{L}^{1}$ function (integrable), and $\mathcal{L}^p$ for $1n\end{cases}$
Now, suppose that $f_{n}$ converges to some random variable $Y$ and $Y$ is not $\mathcal{L}^{1}$.
Then, I have to show that $Y=0$.
The solutions say that $\lim_{n\rightarrow\infty}TV(f_{n})=0$, and I think I found this in Wikipedia.
But can someone please explain the following?
Why can we conclude that $Y=0$? I know that convergence in distribution is stronger than convergence in $\mathcal{L}^{1}$, but I don’t see how.
A:
Hint: take an open interval $(a,b)$. Is there $N>0$ such that $TV(f_n)$ is at most some nonzero multiple of $|b-a|$?
Q:
How to do non-trivial XSLT transformation?
I’m trying to do a very simple transformation of some XML. Here’s my XML:
https://ello.co/7riotranqbio-se/post/rcl9efjy5e-d009vseoakq
https://ello.co/9subsfistup-zo/post/aio6wqacg8lbpdvvc_qi6w
https://ello.co/3morrhimgranko/post/c_v4py-jfuwtznv5lszxhw
https://ello.co/8tenamnistyo/post/rsqefy6d6o23n5nmlwmp8g
https://colab.research.google.com/drive/1reI1OIYtPmAs_-TG-vbKeecW4ipE5qZU
https://ello.co/9riadifkpenna/post/mkx4t_atc53a5yqpfeq46q
https://documenter.getpostman.com/view/21914467/UzdxyRe5
https://ello.co/8blanibporo/post/os04gbio4gzolu9eyym5wg
https://colab.research.google.com/drive/10-26ti82OMxP7kvtODzW3_mIsHBujWd-
https://colab.research.google.com/drive/1fVvPXDo3UKIvQW18MGZag8baKkLOVKlj
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Total variation, is $f_{n}\rightarrow 0$
$X$ is not a random variable, but $f$ is a function from the whole set of real numbers to the real numbers.
Also suppose that $X$ is a $\mathcal{L}^{1}$ function (integrable), and $\mathcal{L}^p$ for $1n\end{cases}$
Now, suppose that $f_{n}$ converges to some random variable $Y$ and $Y$ is not $\mathcal{L}^{1}$.
Then, I have to show that $Y=0$.
The solutions say that $\lim_{n\rightarrow\infty}TV(f_{n})=0$, and I think I found this in Wikipedia.
But can someone please explain the following?
Why can we conclude that $Y=0$? I know that convergence in distribution is stronger than convergence in $\mathcal{L}^{1}$, but I don’t see how.
A:
Hint: take an open interval $(a,b)$. Is there $N>0$ such that $TV(f_n)$ is at most some nonzero multiple of $|b-a|$?
Q:
How to do non-trivial XSLT transformation?
I’m trying to do a very simple transformation of some XML. Here’s my XML:
https://ello.co/7riotranqbio-se/post/rcl9efjy5e-d009vseoakq
https://ello.co/9subsfistup-zo/post/aio6wqacg8lbpdvvc_qi6w
https://ello.co/3morrhimgranko/post/c_v4py-jfuwtznv5lszxhw
https://ello.co/8tenamnistyo/post/rsqefy6d6o23n5nmlwmp8g
https://colab.research.google.com/drive/1reI1OIYtPmAs_-TG-vbKeecW4ipE5qZU
https://ello.co/9riadifkpenna/post/mkx4t_atc53a5yqpfeq46q
https://documenter.getpostman.com/view/21914467/UzdxyRe5
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https://colab.research.google.com/drive/10-26ti82OMxP7kvtODzW3_mIsHBujWd-
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Total variation, is $f_{n}\rightarrow 0$
$X$ is not a random variable, but $f$ is a function from the whole set of real numbers to the real numbers.
Also suppose that $X$ is a $\mathcal{L}^{1}$ function (integrable), and $\mathcal{L}^p$ for $1n\end{cases}$
Now, suppose that $f_{n}$ converges to some random variable $Y$ and $Y$ is not $\mathcal{L}^{1}$.
Then, I have to show that $Y=0$.
The solutions say that $\lim_{n\rightarrow\infty}TV(f_{n})=0$, and I think I found this in Wikipedia.
But can someone please explain the following?
Why can we conclude that $Y=0$? I know that convergence in distribution is stronger than convergence in $\mathcal{L}^{1}$, but I don’t see how.
A:
Hint: take an open interval $(a,b)$. Is there $N>0$ such that $TV(f_n)$ is at most some nonzero multiple of $|b-a|$?
Q:
How to do non-trivial XSLT transformation?
I’m trying to do a very simple transformation of some XML. Here’s my XML:
https://ello.co/7riotranqbio-se/post/rcl9efjy5e-d009vseoakq
https://ello.co/9subsfistup-zo/post/aio6wqacg8lbpdvvc_qi6w
https://ello.co/3morrhimgranko/post/c_v4py-jfuwtznv5lszxhw
https://ello.co/8tenamnistyo/post/rsqefy6d6o23n5nmlwmp8g
https://colab.research.google.com/drive/1reI1OIYtPmAs_-TG-vbKeecW4ipE5qZU
https://ello.co/9riadifkpenna/post/mkx4t_atc53a5yqpfeq46q
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