What is the definition of integrable tensor?

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I just googled 'integrable tensor' but I haven't found any stuff about it. I know this question is silly but the rigid definition is also important. Thanks in advance.



I saw this word here :



Definition Let $Omega$ be an open subset of $mathbbR^d$. A divergence-free positive symmetric tensor is a locally integrable tensor $x mapsto A(x)$ over $Omega$ with the properties that $A(x)in textSym_d^+$ almost everywhere, and $textDivA=0$.



My guess : Each entries of the tensor is integrable.






tensors integrable-systems







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  • Context helps, where did you see this expression ?
    – Nicolas Hemelsoet
    Sep 4 at 9:09










  • @NicolasHemelsoet Thanks for comment I put it in my question.
    – kayak
    Sep 4 at 9:16






  • 1




    I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
    – Kevin
    Sep 4 at 9:41










  • @Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
    – kayak
    Sep 4 at 9:43














up vote
0
down vote

favorite












I just googled 'integrable tensor' but I haven't found any stuff about it. I know this question is silly but the rigid definition is also important. Thanks in advance.



I saw this word here :



Definition Let $Omega$ be an open subset of $mathbbR^d$. A divergence-free positive symmetric tensor is a locally integrable tensor $x mapsto A(x)$ over $Omega$ with the properties that $A(x)in textSym_d^+$ almost everywhere, and $textDivA=0$.



My guess : Each entries of the tensor is integrable.






tensors integrable-systems







share|cite|improve this question























  • Context helps, where did you see this expression ?
    – Nicolas Hemelsoet
    Sep 4 at 9:09










  • @NicolasHemelsoet Thanks for comment I put it in my question.
    – kayak
    Sep 4 at 9:16






  • 1




    I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
    – Kevin
    Sep 4 at 9:41










  • @Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
    – kayak
    Sep 4 at 9:43












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I just googled 'integrable tensor' but I haven't found any stuff about it. I know this question is silly but the rigid definition is also important. Thanks in advance.



I saw this word here :



Definition Let $Omega$ be an open subset of $mathbbR^d$. A divergence-free positive symmetric tensor is a locally integrable tensor $x mapsto A(x)$ over $Omega$ with the properties that $A(x)in textSym_d^+$ almost everywhere, and $textDivA=0$.



My guess : Each entries of the tensor is integrable.






tensors integrable-systems







share|cite|improve this question















I just googled 'integrable tensor' but I haven't found any stuff about it. I know this question is silly but the rigid definition is also important. Thanks in advance.



I saw this word here :



Definition Let $Omega$ be an open subset of $mathbbR^d$. A divergence-free positive symmetric tensor is a locally integrable tensor $x mapsto A(x)$ over $Omega$ with the properties that $A(x)in textSym_d^+$ almost everywhere, and $textDivA=0$.



My guess : Each entries of the tensor is integrable.






tensors integrable-systems




tensors integrable-systems






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 4 at 9:15

























asked Sep 4 at 9:06









kayak

576318




576318











  • Context helps, where did you see this expression ?
    – Nicolas Hemelsoet
    Sep 4 at 9:09










  • @NicolasHemelsoet Thanks for comment I put it in my question.
    – kayak
    Sep 4 at 9:16






  • 1




    I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
    – Kevin
    Sep 4 at 9:41










  • @Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
    – kayak
    Sep 4 at 9:43
















  • Context helps, where did you see this expression ?
    – Nicolas Hemelsoet
    Sep 4 at 9:09










  • @NicolasHemelsoet Thanks for comment I put it in my question.
    – kayak
    Sep 4 at 9:16






  • 1




    I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
    – Kevin
    Sep 4 at 9:41










  • @Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
    – kayak
    Sep 4 at 9:43















Context helps, where did you see this expression ?
– Nicolas Hemelsoet
Sep 4 at 9:09




Context helps, where did you see this expression ?
– Nicolas Hemelsoet
Sep 4 at 9:09












@NicolasHemelsoet Thanks for comment I put it in my question.
– kayak
Sep 4 at 9:16




@NicolasHemelsoet Thanks for comment I put it in my question.
– kayak
Sep 4 at 9:16




1




1




I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
– Kevin
Sep 4 at 9:41




I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
– Kevin
Sep 4 at 9:41












@Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
– kayak
Sep 4 at 9:43




@Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
– kayak
Sep 4 at 9:43















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