About Borel sets and random variables [closed]
1
$$xi, eta - text{Randomvariables}$$
How to show that $forall xi,eta quad {omega midxi(omega) = eta(omega)}$-Borel set?
probability-theory random-variables borel-sets
edited Nov 27 '18 at 10:19
Bernard
118k639112
asked Nov 27 '18 at 10:15
anykkanykk
665
closed as off-topic by Kavi Rama Murthy, NCh, Chinnapparaj R, choco_addicted, Vidyanshu Mishra Nov 29 '18 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Kavi Rama Murthy, Chinnapparaj R, choco_addicted, Vidyanshu Mishra
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1
$$xi, eta - text{Randomvariables}$$
How to show that $forall xi,eta quad {omega midxi(omega) = eta(omega)}$-Borel set?
probability-theory random-variables borel-sets
edited Nov 27 '18 at 10:19
Bernard
118k639112
asked Nov 27 '18 at 10:15
anykkanykk
665
closed as off-topic by Kavi Rama Murthy, NCh, Chinnapparaj R, choco_addicted, Vidyanshu Mishra Nov 29 '18 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Kavi Rama Murthy, Chinnapparaj R, choco_addicted, Vidyanshu Mishra
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
1
1
1
$$xi, eta - text{Randomvariables}$$
How to show that $forall xi,eta quad {omega midxi(omega) = eta(omega)}$-Borel set?
probability-theory random-variables borel-sets
edited Nov 27 '18 at 10:19
Bernard
118k639112
asked Nov 27 '18 at 10:15
anykkanykk
665
$$xi, eta - text{Randomvariables}$$
How to show that $forall xi,eta quad {omega midxi(omega) = eta(omega)}$-Borel set?
probability-theory random-variables borel-sets
probability-theory random-variables borel-sets
edited Nov 27 '18 at 10:19
Bernard
118k639112
asked Nov 27 '18 at 10:15
anykkanykk
665
edited Nov 27 '18 at 10:19
Bernard
118k639112
asked Nov 27 '18 at 10:15
anykkanykk
665
edited Nov 27 '18 at 10:19
Bernard
118k639112
edited Nov 27 '18 at 10:19
Bernard
118k639112
edited Nov 27 '18 at 10:19
Bernard
118k639112
118k639112
asked Nov 27 '18 at 10:15
anykkanykk
665
asked Nov 27 '18 at 10:15
anykkanykk
665
asked Nov 27 '18 at 10:15
anykkanykk
665
665
closed as off-topic by Kavi Rama Murthy, NCh, Chinnapparaj R, choco_addicted, Vidyanshu Mishra Nov 29 '18 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Kavi Rama Murthy, Chinnapparaj R, choco_addicted, Vidyanshu Mishra
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Kavi Rama Murthy, NCh, Chinnapparaj R, choco_addicted, Vidyanshu Mishra Nov 29 '18 at 8:13
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Kavi Rama Murthy, Chinnapparaj R, choco_addicted, Vidyanshu Mishra
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
1
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oldest
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1
$xi -eta$ is a a random variable so $(xi-eta)^{-1} {0}$ is measurable.
answered Nov 27 '18 at 10:18
Kavi Rama MurthyKavi Rama Murthy
51.5k31955
That $xi - eta$ is random variable is ok, $(xi - eta)^{-1}({0})={omega | (xi - eta)(omega) = 0} in mathcal F$, but why it is Borel set?
– anykk
Nov 27 '18 at 19:21
Where are your random variables defined? If they are defined on a general probability space there is no such thing as Borel set in the sample space and your question does not make sense.
– Kavi Rama Murthy
Nov 27 '18 at 23:05
In my problem clearly it does not define, where it is, but I can try to determine for myself.
– anykk
Nov 28 '18 at 3:30
It will be, when $(mathbb R, mathcal B (mathbb R), mathbb P)$? $mathcal B (mathbb R)$ is Borel algebra
– anykk
Nov 28 '18 at 3:41
In that case what is your question? If $f$ is measurable on this space then the inverse image of any Borel set is a Borel set by definition. So $(xi -eta)^{-1}({0})$ is a Borel set. I have no idea where your confusion is. @anykk
– Kavi Rama Murthy
Nov 28 '18 at 5:16
|
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
1
$xi -eta$ is a a random variable so $(xi-eta)^{-1} {0}$ is measurable.
answered Nov 27 '18 at 10:18
Kavi Rama MurthyKavi Rama Murthy
51.5k31955
That $xi - eta$ is random variable is ok, $(xi - eta)^{-1}({0})={omega | (xi - eta)(omega) = 0} in mathcal F$, but why it is Borel set?
– anykk
Nov 27 '18 at 19:21
Where are your random variables defined? If they are defined on a general probability space there is no such thing as Borel set in the sample space and your question does not make sense.
– Kavi Rama Murthy
Nov 27 '18 at 23:05
In my problem clearly it does not define, where it is, but I can try to determine for myself.
– anykk
Nov 28 '18 at 3:30
It will be, when $(mathbb R, mathcal B (mathbb R), mathbb P)$? $mathcal B (mathbb R)$ is Borel algebra
– anykk
Nov 28 '18 at 3:41
In that case what is your question? If $f$ is measurable on this space then the inverse image of any Borel set is a Borel set by definition. So $(xi -eta)^{-1}({0})$ is a Borel set. I have no idea where your confusion is. @anykk
– Kavi Rama Murthy
Nov 28 '18 at 5:16
|
show 1 more comment
1
$xi -eta$ is a a random variable so $(xi-eta)^{-1} {0}$ is measurable.
answered Nov 27 '18 at 10:18
Kavi Rama MurthyKavi Rama Murthy
51.5k31955
That $xi - eta$ is random variable is ok, $(xi - eta)^{-1}({0})={omega | (xi - eta)(omega) = 0} in mathcal F$, but why it is Borel set?
– anykk
Nov 27 '18 at 19:21
Where are your random variables defined? If they are defined on a general probability space there is no such thing as Borel set in the sample space and your question does not make sense.
– Kavi Rama Murthy
Nov 27 '18 at 23:05
In my problem clearly it does not define, where it is, but I can try to determine for myself.
– anykk
Nov 28 '18 at 3:30
It will be, when $(mathbb R, mathcal B (mathbb R), mathbb P)$? $mathcal B (mathbb R)$ is Borel algebra
– anykk
Nov 28 '18 at 3:41
In that case what is your question? If $f$ is measurable on this space then the inverse image of any Borel set is a Borel set by definition. So $(xi -eta)^{-1}({0})$ is a Borel set. I have no idea where your confusion is. @anykk
– Kavi Rama Murthy
Nov 28 '18 at 5:16
|
show 1 more comment
1
1
1
$xi -eta$ is a a random variable so $(xi-eta)^{-1} {0}$ is measurable.
answered Nov 27 '18 at 10:18
Kavi Rama MurthyKavi Rama Murthy
51.5k31955
$xi -eta$ is a a random variable so $(xi-eta)^{-1} {0}$ is measurable.
answered Nov 27 '18 at 10:18
Kavi Rama MurthyKavi Rama Murthy
51.5k31955
answered Nov 27 '18 at 10:18
Kavi Rama MurthyKavi Rama Murthy
51.5k31955
answered Nov 27 '18 at 10:18
Kavi Rama MurthyKavi Rama Murthy
51.5k31955
answered Nov 27 '18 at 10:18
Kavi Rama MurthyKavi Rama Murthy
51.5k31955
51.5k31955
That $xi - eta$ is random variable is ok, $(xi - eta)^{-1}({0})={omega | (xi - eta)(omega) = 0} in mathcal F$, but why it is Borel set?
– anykk
Nov 27 '18 at 19:21
Where are your random variables defined? If they are defined on a general probability space there is no such thing as Borel set in the sample space and your question does not make sense.
– Kavi Rama Murthy
Nov 27 '18 at 23:05
In my problem clearly it does not define, where it is, but I can try to determine for myself.
– anykk
Nov 28 '18 at 3:30
It will be, when $(mathbb R, mathcal B (mathbb R), mathbb P)$? $mathcal B (mathbb R)$ is Borel algebra
– anykk
Nov 28 '18 at 3:41
In that case what is your question? If $f$ is measurable on this space then the inverse image of any Borel set is a Borel set by definition. So $(xi -eta)^{-1}({0})$ is a Borel set. I have no idea where your confusion is. @anykk
– Kavi Rama Murthy
Nov 28 '18 at 5:16
|
show 1 more comment
That $xi - eta$ is random variable is ok, $(xi - eta)^{-1}({0})={omega | (xi - eta)(omega) = 0} in mathcal F$, but why it is Borel set?
– anykk
Nov 27 '18 at 19:21
Where are your random variables defined? If they are defined on a general probability space there is no such thing as Borel set in the sample space and your question does not make sense.
– Kavi Rama Murthy
Nov 27 '18 at 23:05
In my problem clearly it does not define, where it is, but I can try to determine for myself.
– anykk
Nov 28 '18 at 3:30
It will be, when $(mathbb R, mathcal B (mathbb R), mathbb P)$? $mathcal B (mathbb R)$ is Borel algebra
– anykk
Nov 28 '18 at 3:41
In that case what is your question? If $f$ is measurable on this space then the inverse image of any Borel set is a Borel set by definition. So $(xi -eta)^{-1}({0})$ is a Borel set. I have no idea where your confusion is. @anykk
– Kavi Rama Murthy
Nov 28 '18 at 5:16
That $xi - eta$ is random variable is ok, $(xi - eta)^{-1}({0})={omega | (xi - eta)(omega) = 0} in mathcal F$, but why it is Borel set?
– anykk
Nov 27 '18 at 19:21
That $xi - eta$ is random variable is ok, $(xi - eta)^{-1}({0})={omega | (xi - eta)(omega) = 0} in mathcal F$, but why it is Borel set?
– anykk
Nov 27 '18 at 19:21
Where are your random variables defined? If they are defined on a general probability space there is no such thing as Borel set in the sample space and your question does not make sense.
– Kavi Rama Murthy
Nov 27 '18 at 23:05
Where are your random variables defined? If they are defined on a general probability space there is no such thing as Borel set in the sample space and your question does not make sense.
– Kavi Rama Murthy
Nov 27 '18 at 23:05
In my problem clearly it does not define, where it is, but I can try to determine for myself.
– anykk
Nov 28 '18 at 3:30
In my problem clearly it does not define, where it is, but I can try to determine for myself.
– anykk
Nov 28 '18 at 3:30
It will be, when $(mathbb R, mathcal B (mathbb R), mathbb P)$? $mathcal B (mathbb R)$ is Borel algebra
– anykk
Nov 28 '18 at 3:41
It will be, when $(mathbb R, mathcal B (mathbb R), mathbb P)$? $mathcal B (mathbb R)$ is Borel algebra
– anykk
Nov 28 '18 at 3:41
In that case what is your question? If $f$ is measurable on this space then the inverse image of any Borel set is a Borel set by definition. So $(xi -eta)^{-1}({0})$ is a Borel set. I have no idea where your confusion is. @anykk
– Kavi Rama Murthy
Nov 28 '18 at 5:16
In that case what is your question? If $f$ is measurable on this space then the inverse image of any Borel set is a Borel set by definition. So $(xi -eta)^{-1}({0})$ is a Borel set. I have no idea where your confusion is. @anykk
– Kavi Rama Murthy
Nov 28 '18 at 5:16
|
show 1 more comment
