Non-product measure proof of Fubini’s theorem [on hold]
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Can you state/direct me to a proof of Fubini’s theorem that does not rely on product measure ?
integration improper-integrals lebesgue-integral indefinite-integrals complex-integration
asked Nov 15 at 18:33
user472374
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put on hold as off-topic by projectilemotion, jgon, user10354138, Davide Giraudo, amWhy Nov 16 at 14:51
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." – projectilemotion, user10354138, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
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Can you state/direct me to a proof of Fubini’s theorem that does not rely on product measure ?
integration improper-integrals lebesgue-integral indefinite-integrals complex-integration
asked Nov 15 at 18:33
user472374
123
put on hold as off-topic by projectilemotion, jgon, user10354138, Davide Giraudo, amWhy Nov 16 at 14:51
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." – projectilemotion, user10354138, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
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It seems that the entire theorem is about proving something about integrals with respect to the product measure. Why would you want to learn it without the product measure?
– rubikscube09
Nov 15 at 18:42
@rubikscube09 I more or less agree with you. The only interpretation I can come up with is perhaps the OP wants a proof of Tonelli's theorem (iterated integrals of a nonnegative function agree with the integral wrt product measure) which doesn't reference the product measure. (Which would at least be conceivable, since one could restrict the statement to iterated integrals of a nonnegative function agree with each other). The tags are also weird on this one, since improper integrals, indefinite integrals, and complex integration don't really seem to apply here.
– jgon
Nov 16 at 3:34
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up vote
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down vote
favorite
Can you state/direct me to a proof of Fubini’s theorem that does not rely on product measure ?
integration improper-integrals lebesgue-integral indefinite-integrals complex-integration
asked Nov 15 at 18:33
user472374
123
Can you state/direct me to a proof of Fubini’s theorem that does not rely on product measure ?
integration improper-integrals lebesgue-integral indefinite-integrals complex-integration
integration improper-integrals lebesgue-integral indefinite-integrals complex-integration
asked Nov 15 at 18:33
user472374
123
asked Nov 15 at 18:33
user472374
123
asked Nov 15 at 18:33
user472374
123
asked Nov 15 at 18:33
user472374
123
asked Nov 15 at 18:33
user472374
123
123
put on hold as off-topic by projectilemotion, jgon, user10354138, Davide Giraudo, amWhy Nov 16 at 14:51
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." – projectilemotion, user10354138, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by projectilemotion, jgon, user10354138, Davide Giraudo, amWhy Nov 16 at 14:51
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." – projectilemotion, user10354138, amWhy
If this question can be reworded to fit the rules in the help center, please edit the question.
5
It seems that the entire theorem is about proving something about integrals with respect to the product measure. Why would you want to learn it without the product measure?
– rubikscube09
Nov 15 at 18:42
@rubikscube09 I more or less agree with you. The only interpretation I can come up with is perhaps the OP wants a proof of Tonelli's theorem (iterated integrals of a nonnegative function agree with the integral wrt product measure) which doesn't reference the product measure. (Which would at least be conceivable, since one could restrict the statement to iterated integrals of a nonnegative function agree with each other). The tags are also weird on this one, since improper integrals, indefinite integrals, and complex integration don't really seem to apply here.
– jgon
Nov 16 at 3:34
add a comment |
5
It seems that the entire theorem is about proving something about integrals with respect to the product measure. Why would you want to learn it without the product measure?
– rubikscube09
Nov 15 at 18:42
@rubikscube09 I more or less agree with you. The only interpretation I can come up with is perhaps the OP wants a proof of Tonelli's theorem (iterated integrals of a nonnegative function agree with the integral wrt product measure) which doesn't reference the product measure. (Which would at least be conceivable, since one could restrict the statement to iterated integrals of a nonnegative function agree with each other). The tags are also weird on this one, since improper integrals, indefinite integrals, and complex integration don't really seem to apply here.
– jgon
Nov 16 at 3:34
5
5
It seems that the entire theorem is about proving something about integrals with respect to the product measure. Why would you want to learn it without the product measure?
– rubikscube09
Nov 15 at 18:42
It seems that the entire theorem is about proving something about integrals with respect to the product measure. Why would you want to learn it without the product measure?
– rubikscube09
Nov 15 at 18:42
@rubikscube09 I more or less agree with you. The only interpretation I can come up with is perhaps the OP wants a proof of Tonelli's theorem (iterated integrals of a nonnegative function agree with the integral wrt product measure) which doesn't reference the product measure. (Which would at least be conceivable, since one could restrict the statement to iterated integrals of a nonnegative function agree with each other). The tags are also weird on this one, since improper integrals, indefinite integrals, and complex integration don't really seem to apply here.
– jgon
Nov 16 at 3:34
@rubikscube09 I more or less agree with you. The only interpretation I can come up with is perhaps the OP wants a proof of Tonelli's theorem (iterated integrals of a nonnegative function agree with the integral wrt product measure) which doesn't reference the product measure. (Which would at least be conceivable, since one could restrict the statement to iterated integrals of a nonnegative function agree with each other). The tags are also weird on this one, since improper integrals, indefinite integrals, and complex integration don't really seem to apply here.
– jgon
Nov 16 at 3:34
add a comment |
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5
It seems that the entire theorem is about proving something about integrals with respect to the product measure. Why would you want to learn it without the product measure?
– rubikscube09
Nov 15 at 18:42
@rubikscube09 I more or less agree with you. The only interpretation I can come up with is perhaps the OP wants a proof of Tonelli's theorem (iterated integrals of a nonnegative function agree with the integral wrt product measure) which doesn't reference the product measure. (Which would at least be conceivable, since one could restrict the statement to iterated integrals of a nonnegative function agree with each other). The tags are also weird on this one, since improper integrals, indefinite integrals, and complex integration don't really seem to apply here.
– jgon
Nov 16 at 3:34