Inverse of Borel set is measurable?
Just a short question.
I was reading this thread and got a question about one of the comments. In the second answer, @geekazoid said that
Also, $h−g$ is measurable, and ${0}$ is a Borel set, so $(h−g)^{−1}(0)$ is measurable.
The question is that why he mentioned about ${0}$ is a Borel set.
(Since I don't have enough reputation, I cannot but to make another question.)
measure-theory lebesgue-measure borel-sets
asked Nov 26 at 11:55
Yong Jin Shin
132
add a comment |
Just a short question.
I was reading this thread and got a question about one of the comments. In the second answer, @geekazoid said that
Also, $h−g$ is measurable, and ${0}$ is a Borel set, so $(h−g)^{−1}(0)$ is measurable.
The question is that why he mentioned about ${0}$ is a Borel set.
(Since I don't have enough reputation, I cannot but to make another question.)
measure-theory lebesgue-measure borel-sets
asked Nov 26 at 11:55
Yong Jin Shin
132
Measurable means inverse image of any Borel set is measurable.
– Kavi Rama Murthy
Nov 26 at 11:59
add a comment |
Just a short question.
I was reading this thread and got a question about one of the comments. In the second answer, @geekazoid said that
Also, $h−g$ is measurable, and ${0}$ is a Borel set, so $(h−g)^{−1}(0)$ is measurable.
The question is that why he mentioned about ${0}$ is a Borel set.
(Since I don't have enough reputation, I cannot but to make another question.)
measure-theory lebesgue-measure borel-sets
asked Nov 26 at 11:55
Yong Jin Shin
132
Just a short question.
I was reading this thread and got a question about one of the comments. In the second answer, @geekazoid said that
Also, $h−g$ is measurable, and ${0}$ is a Borel set, so $(h−g)^{−1}(0)$ is measurable.
The question is that why he mentioned about ${0}$ is a Borel set.
(Since I don't have enough reputation, I cannot but to make another question.)
measure-theory lebesgue-measure borel-sets
measure-theory lebesgue-measure borel-sets
asked Nov 26 at 11:55
Yong Jin Shin
132
asked Nov 26 at 11:55
Yong Jin Shin
132
asked Nov 26 at 11:55
Yong Jin Shin
132
asked Nov 26 at 11:55
Yong Jin Shin
132
asked Nov 26 at 11:55
Yong Jin Shin
132
132
Measurable means inverse image of any Borel set is measurable.
– Kavi Rama Murthy
Nov 26 at 11:59
add a comment |
Measurable means inverse image of any Borel set is measurable.
– Kavi Rama Murthy
Nov 26 at 11:59
Measurable means inverse image of any Borel set is measurable.
– Kavi Rama Murthy
Nov 26 at 11:59
Measurable means inverse image of any Borel set is measurable.
– Kavi Rama Murthy
Nov 26 at 11:59
add a comment |
1 Answer
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Since $B:={0}$ is Borel and $h-g$ is measurable, $(h-g)^{-1}(B)$ is Borel - measurable.
Use the Definitions of "Borel set" and "measurable function" !
answered Nov 26 at 12:21
Fred
44.2k1645
Thank you for your answer!
– Yong Jin Shin
Nov 26 at 12:30
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Since $B:={0}$ is Borel and $h-g$ is measurable, $(h-g)^{-1}(B)$ is Borel - measurable.
Use the Definitions of "Borel set" and "measurable function" !
answered Nov 26 at 12:21
Fred
44.2k1645
Thank you for your answer!
– Yong Jin Shin
Nov 26 at 12:30
add a comment |
Since $B:={0}$ is Borel and $h-g$ is measurable, $(h-g)^{-1}(B)$ is Borel - measurable.
Use the Definitions of "Borel set" and "measurable function" !
answered Nov 26 at 12:21
Fred
44.2k1645
Thank you for your answer!
– Yong Jin Shin
Nov 26 at 12:30
add a comment |
Since $B:={0}$ is Borel and $h-g$ is measurable, $(h-g)^{-1}(B)$ is Borel - measurable.
Use the Definitions of "Borel set" and "measurable function" !
answered Nov 26 at 12:21
Fred
44.2k1645
Since $B:={0}$ is Borel and $h-g$ is measurable, $(h-g)^{-1}(B)$ is Borel - measurable.
Use the Definitions of "Borel set" and "measurable function" !
answered Nov 26 at 12:21
Fred
44.2k1645
answered Nov 26 at 12:21
Fred
44.2k1645
answered Nov 26 at 12:21
Fred
44.2k1645
answered Nov 26 at 12:21
Fred
44.2k1645
44.2k1645
Thank you for your answer!
– Yong Jin Shin
Nov 26 at 12:30
add a comment |
Thank you for your answer!
– Yong Jin Shin
Nov 26 at 12:30
Thank you for your answer!
– Yong Jin Shin
Nov 26 at 12:30
Thank you for your answer!
– Yong Jin Shin
Nov 26 at 12:30
add a comment |
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Measurable means inverse image of any Borel set is measurable.
– Kavi Rama Murthy
Nov 26 at 11:59