Mixing
Does bounded limits of one integral imply that the double integral is bounded?
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I know that Fubini's theorem means that the one may switch the oder of integration if the double integral yields a finite value when the integrand is replaced by its absolute value.
But I have also heard that if one of the integrals has limits which are bounded, then the double integral is bounded, too:
Is the following true?
($|a|neinfty, and |b|neinfty$) or ($|c|neinfty, and |d|neinfty$) $implies$ $int_{mathbf{a}}^{mathbf{b}} int_{mathbf{c}}^{mathbf{d}} |f(x)|<infty$
But I don't think this is true, because the limits might be bounded, but the integrand could be something like the Dirac delta, in which cases the integration does not yield something finite...
Does bounded limits of one integral imply that the double integral is bounded?
real-analysis calculus integration definite-integrals
asked Jan 28 at 9:18
guimptionguimption
1409
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add a comment |
$begingroup$
I know that Fubini's theorem means that the one may switch the oder of integration if the double integral yields a finite value when the integrand is replaced by its absolute value.
But I have also heard that if one of the integrals has limits which are bounded, then the double integral is bounded, too:
Is the following true?
($|a|neinfty, and |b|neinfty$) or ($|c|neinfty, and |d|neinfty$) $implies$ $int_{mathbf{a}}^{mathbf{b}} int_{mathbf{c}}^{mathbf{d}} |f(x)|<infty$
But I don't think this is true, because the limits might be bounded, but the integrand could be something like the Dirac delta, in which cases the integration does not yield something finite...
Does bounded limits of one integral imply that the double integral is bounded?
real-analysis calculus integration definite-integrals
asked Jan 28 at 9:18
guimptionguimption
1409
$endgroup$
2
$begingroup$
Can you state your question more clearly using symbols?
$endgroup$
– Kavi Rama Murthy
Jan 28 at 9:21
1
$begingroup$
Here is [an introduction to posting mathematical notation](). When you refer to "limits" that "one of the integrals has", it is unclear whether you are thinking of the limits of integration (region over which the integral is taken) or bounds on the the integrand. Your Question would be improved by introducing notation that will clarify your meaning.
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– hardmath
Jan 29 at 22:51
$begingroup$
I'm still new at this, but I did my best to modify the question let me know if it is better plaese
$endgroup$
– guimption
Jan 31 at 7:43
add a comment |
$begingroup$
I know that Fubini's theorem means that the one may switch the oder of integration if the double integral yields a finite value when the integrand is replaced by its absolute value.
But I have also heard that if one of the integrals has limits which are bounded, then the double integral is bounded, too:
Is the following true?
($|a|neinfty, and |b|neinfty$) or ($|c|neinfty, and |d|neinfty$) $implies$ $int_{mathbf{a}}^{mathbf{b}} int_{mathbf{c}}^{mathbf{d}} |f(x)|<infty$
But I don't think this is true, because the limits might be bounded, but the integrand could be something like the Dirac delta, in which cases the integration does not yield something finite...
Does bounded limits of one integral imply that the double integral is bounded?
real-analysis calculus integration definite-integrals
asked Jan 28 at 9:18
guimptionguimption
1409
$endgroup$
I know that Fubini's theorem means that the one may switch the oder of integration if the double integral yields a finite value when the integrand is replaced by its absolute value.
But I have also heard that if one of the integrals has limits which are bounded, then the double integral is bounded, too:
Is the following true?
($|a|neinfty, and |b|neinfty$) or ($|c|neinfty, and |d|neinfty$) $implies$ $int_{mathbf{a}}^{mathbf{b}} int_{mathbf{c}}^{mathbf{d}} |f(x)|<infty$
But I don't think this is true, because the limits might be bounded, but the integrand could be something like the Dirac delta, in which cases the integration does not yield something finite...
Does bounded limits of one integral imply that the double integral is bounded?
real-analysis calculus integration definite-integrals
real-analysis calculus integration definite-integrals
asked Jan 28 at 9:18
guimptionguimption
1409
asked Jan 28 at 9:18
guimptionguimption
1409
edited Jan 31 at 7:43
guimption
asked Jan 28 at 9:18
guimptionguimption
1409
asked Jan 28 at 9:18
guimptionguimption
1409
asked Jan 28 at 9:18
guimptionguimption
1409
1409
2
$begingroup$
Can you state your question more clearly using symbols?
$endgroup$
– Kavi Rama Murthy
Jan 28 at 9:21
1
$begingroup$
Here is [an introduction to posting mathematical notation](). When you refer to "limits" that "one of the integrals has", it is unclear whether you are thinking of the limits of integration (region over which the integral is taken) or bounds on the the integrand. Your Question would be improved by introducing notation that will clarify your meaning.
$endgroup$
– hardmath
Jan 29 at 22:51
$begingroup$
I'm still new at this, but I did my best to modify the question let me know if it is better plaese
$endgroup$
– guimption
Jan 31 at 7:43
add a comment |
2
$begingroup$
Can you state your question more clearly using symbols?
$endgroup$
– Kavi Rama Murthy
Jan 28 at 9:21
1
$begingroup$
Here is [an introduction to posting mathematical notation](). When you refer to "limits" that "one of the integrals has", it is unclear whether you are thinking of the limits of integration (region over which the integral is taken) or bounds on the the integrand. Your Question would be improved by introducing notation that will clarify your meaning.
$endgroup$
– hardmath
Jan 29 at 22:51
$begingroup$
I'm still new at this, but I did my best to modify the question let me know if it is better plaese
$endgroup$
– guimption
Jan 31 at 7:43
2
2
$begingroup$
Can you state your question more clearly using symbols?
$endgroup$
– Kavi Rama Murthy
Jan 28 at 9:21
$begingroup$
Can you state your question more clearly using symbols?
$endgroup$
– Kavi Rama Murthy
Jan 28 at 9:21
1
1
$begingroup$
Here is [an introduction to posting mathematical notation](). When you refer to "limits" that "one of the integrals has", it is unclear whether you are thinking of the limits of integration (region over which the integral is taken) or bounds on the the integrand. Your Question would be improved by introducing notation that will clarify your meaning.
$endgroup$
– hardmath
Jan 29 at 22:51
$begingroup$
Here is [an introduction to posting mathematical notation](). When you refer to "limits" that "one of the integrals has", it is unclear whether you are thinking of the limits of integration (region over which the integral is taken) or bounds on the the integrand. Your Question would be improved by introducing notation that will clarify your meaning.
$endgroup$
– hardmath
Jan 29 at 22:51
$begingroup$
I'm still new at this, but I did my best to modify the question let me know if it is better plaese
$endgroup$
– guimption
Jan 31 at 7:43
$begingroup$
I'm still new at this, but I did my best to modify the question let me know if it is better plaese
$endgroup$
– guimption
Jan 31 at 7:43
add a comment |
0
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2
$begingroup$
Can you state your question more clearly using symbols?
$endgroup$
– Kavi Rama Murthy
Jan 28 at 9:21
1
$begingroup$
Here is [an introduction to posting mathematical notation](). When you refer to "limits" that "one of the integrals has", it is unclear whether you are thinking of the limits of integration (region over which the integral is taken) or bounds on the the integrand. Your Question would be improved by introducing notation that will clarify your meaning.
$endgroup$
– hardmath
Jan 29 at 22:51
$begingroup$
I'm still new at this, but I did my best to modify the question let me know if it is better plaese
$endgroup$
– guimption
Jan 31 at 7:43