notation - what does this $wedge$ inside the integral mean?Why is $wedge$ a minimum and $vee$ a maximum?What...
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notation - what does this $wedge$ inside the integral mean?
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$begingroup$
I have this integral:
$int(epsilon wedge |x|^{2})nu(dx)$
The $wedge$ symbol means that I have to integrate $|x|^{2}$ when $|x|>epsilon$ or when $|x|>1$?
real-analysis calculus integration notation lebesgue-integral
edited yesterday
Arnaud Mortier
20.2k22261
asked yesterday
MkDMkD
82
New contributor
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I have this integral:
$int(epsilon wedge |x|^{2})nu(dx)$
The $wedge$ symbol means that I have to integrate $|x|^{2}$ when $|x|>epsilon$ or when $|x|>1$?
real-analysis calculus integration notation lebesgue-integral
edited yesterday
Arnaud Mortier
20.2k22261
asked yesterday
MkDMkD
82
New contributor
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Related: math.stackexchange.com/questions/1839344/…
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
Simply put, it refers to the "minimum", i.e. $aland b = min(a,b)$.
$endgroup$
– Minus One-Twelfth
yesterday
$begingroup$
It is a notation borrowed from Lattice theory, occasionally used in some approaches to measure theory: specifically $$begin{split}wedgeequivtext{ "meet"}&implies awedge b=min(a,b)\ veeequivtext{ "join"},,&implies avee b=max(a,b)end{split}text{ if }a,binBbb R.$$
$endgroup$
– Daniele Tampieri
yesterday
add a comment |
$begingroup$
I have this integral:
$int(epsilon wedge |x|^{2})nu(dx)$
The $wedge$ symbol means that I have to integrate $|x|^{2}$ when $|x|>epsilon$ or when $|x|>1$?
real-analysis calculus integration notation lebesgue-integral
edited yesterday
Arnaud Mortier
20.2k22261
asked yesterday
MkDMkD
82
New contributor
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have this integral:
$int(epsilon wedge |x|^{2})nu(dx)$
The $wedge$ symbol means that I have to integrate $|x|^{2}$ when $|x|>epsilon$ or when $|x|>1$?
real-analysis calculus integration notation lebesgue-integral
real-analysis calculus integration notation lebesgue-integral
edited yesterday
Arnaud Mortier
20.2k22261
asked yesterday
MkDMkD
82
New contributor
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Arnaud Mortier
20.2k22261
asked yesterday
MkDMkD
82
New contributor
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Arnaud Mortier
20.2k22261
edited yesterday
Arnaud Mortier
20.2k22261
edited yesterday
Arnaud Mortier
20.2k22261
20.2k22261
asked yesterday
MkDMkD
82
New contributor
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
MkDMkD
82
asked yesterday
MkDMkD
82
82
New contributor
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
MkD is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Related: math.stackexchange.com/questions/1839344/…
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
Simply put, it refers to the "minimum", i.e. $aland b = min(a,b)$.
$endgroup$
– Minus One-Twelfth
yesterday
$begingroup$
It is a notation borrowed from Lattice theory, occasionally used in some approaches to measure theory: specifically $$begin{split}wedgeequivtext{ "meet"}&implies awedge b=min(a,b)\ veeequivtext{ "join"},,&implies avee b=max(a,b)end{split}text{ if }a,binBbb R.$$
$endgroup$
– Daniele Tampieri
yesterday
add a comment |
$begingroup$
Related: math.stackexchange.com/questions/1839344/…
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
Simply put, it refers to the "minimum", i.e. $aland b = min(a,b)$.
$endgroup$
– Minus One-Twelfth
yesterday
$begingroup$
It is a notation borrowed from Lattice theory, occasionally used in some approaches to measure theory: specifically $$begin{split}wedgeequivtext{ "meet"}&implies awedge b=min(a,b)\ veeequivtext{ "join"},,&implies avee b=max(a,b)end{split}text{ if }a,binBbb R.$$
$endgroup$
– Daniele Tampieri
yesterday
$begingroup$
Related: math.stackexchange.com/questions/1839344/…
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
Related: math.stackexchange.com/questions/1839344/…
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
Simply put, it refers to the "minimum", i.e. $aland b = min(a,b)$.
$endgroup$
– Minus One-Twelfth
yesterday
$begingroup$
Simply put, it refers to the "minimum", i.e. $aland b = min(a,b)$.
$endgroup$
– Minus One-Twelfth
yesterday
$begingroup$
It is a notation borrowed from Lattice theory, occasionally used in some approaches to measure theory: specifically $$begin{split}wedgeequivtext{ "meet"}&implies awedge b=min(a,b)\ veeequivtext{ "join"},,&implies avee b=max(a,b)end{split}text{ if }a,binBbb R.$$
$endgroup$
– Daniele Tampieri
yesterday
$begingroup$
It is a notation borrowed from Lattice theory, occasionally used in some approaches to measure theory: specifically $$begin{split}wedgeequivtext{ "meet"}&implies awedge b=min(a,b)\ veeequivtext{ "join"},,&implies avee b=max(a,b)end{split}text{ if }a,binBbb R.$$
$endgroup$
– Daniele Tampieri
yesterday
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The wedge stands for minimum. $awedge b=min{a,b}$. The integral is $int_{{|x||^{2} geq epsilon}} epsilon nu (dx)+int_{{|x||^{2} < epsilon}} |x|^{2} nu (dx)$.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42867
$endgroup$
5
$begingroup$
It would be perhaps easier to read if you added a line at the beginning to indicate that $wedge$ means $min$.
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
@ArnaudMortier Thanks for the comment.
$endgroup$
– Kavi Rama Murthy
yesterday
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
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active
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votes
$begingroup$
The wedge stands for minimum. $awedge b=min{a,b}$. The integral is $int_{{|x||^{2} geq epsilon}} epsilon nu (dx)+int_{{|x||^{2} < epsilon}} |x|^{2} nu (dx)$.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42867
$endgroup$
5
$begingroup$
It would be perhaps easier to read if you added a line at the beginning to indicate that $wedge$ means $min$.
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
@ArnaudMortier Thanks for the comment.
$endgroup$
– Kavi Rama Murthy
yesterday
add a comment |
$begingroup$
The wedge stands for minimum. $awedge b=min{a,b}$. The integral is $int_{{|x||^{2} geq epsilon}} epsilon nu (dx)+int_{{|x||^{2} < epsilon}} |x|^{2} nu (dx)$.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42867
$endgroup$
5
$begingroup$
It would be perhaps easier to read if you added a line at the beginning to indicate that $wedge$ means $min$.
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
@ArnaudMortier Thanks for the comment.
$endgroup$
– Kavi Rama Murthy
yesterday
add a comment |
$begingroup$
The wedge stands for minimum. $awedge b=min{a,b}$. The integral is $int_{{|x||^{2} geq epsilon}} epsilon nu (dx)+int_{{|x||^{2} < epsilon}} |x|^{2} nu (dx)$.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42867
$endgroup$
The wedge stands for minimum. $awedge b=min{a,b}$. The integral is $int_{{|x||^{2} geq epsilon}} epsilon nu (dx)+int_{{|x||^{2} < epsilon}} |x|^{2} nu (dx)$.
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42867
edited yesterday
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42867
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42867
answered yesterday
Kavi Rama MurthyKavi Rama Murthy
65.8k42867
65.8k42867
5
$begingroup$
It would be perhaps easier to read if you added a line at the beginning to indicate that $wedge$ means $min$.
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
@ArnaudMortier Thanks for the comment.
$endgroup$
– Kavi Rama Murthy
yesterday
add a comment |
5
$begingroup$
It would be perhaps easier to read if you added a line at the beginning to indicate that $wedge$ means $min$.
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
@ArnaudMortier Thanks for the comment.
$endgroup$
– Kavi Rama Murthy
yesterday
5
5
$begingroup$
It would be perhaps easier to read if you added a line at the beginning to indicate that $wedge$ means $min$.
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
It would be perhaps easier to read if you added a line at the beginning to indicate that $wedge$ means $min$.
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
@ArnaudMortier Thanks for the comment.
$endgroup$
– Kavi Rama Murthy
yesterday
$begingroup$
@ArnaudMortier Thanks for the comment.
$endgroup$
– Kavi Rama Murthy
yesterday
add a comment |
MkD is a new contributor. Be nice, and check out our Code of Conduct.
MkD is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
Related: math.stackexchange.com/questions/1839344/…
$endgroup$
– Arnaud Mortier
yesterday
$begingroup$
Simply put, it refers to the "minimum", i.e. $aland b = min(a,b)$.
$endgroup$
– Minus One-Twelfth
yesterday
$begingroup$
It is a notation borrowed from Lattice theory, occasionally used in some approaches to measure theory: specifically $$begin{split}wedgeequivtext{ "meet"}&implies awedge b=min(a,b)\ veeequivtext{ "join"},,&implies avee b=max(a,b)end{split}text{ if }a,binBbb R.$$
$endgroup$
– Daniele Tampieri
yesterday