Why the product of measure is a tensor product?











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Let $mu$ and $nu$ two measure. What is the justification to say that the measure product is a tensor product ? i.e. why $mutimes nu$ is written $muotimes nu$ ? (Of course, beside the fact that is by definition or it's just a notation). Our teacher told us that the reason that we write it as a tensor product it's because it behave as a tensor product). But I don't understand this (I'm not very confortable with tensor product).










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  • For example, assuming $sigma$-finiteness, $L^1(muotimesnu)=L^1(mu)otimes L^1(nu)$ as Banach spaces.
    – user10354138
    Nov 13 at 13:58















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Let $mu$ and $nu$ two measure. What is the justification to say that the measure product is a tensor product ? i.e. why $mutimes nu$ is written $muotimes nu$ ? (Of course, beside the fact that is by definition or it's just a notation). Our teacher told us that the reason that we write it as a tensor product it's because it behave as a tensor product). But I don't understand this (I'm not very confortable with tensor product).










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  • For example, assuming $sigma$-finiteness, $L^1(muotimesnu)=L^1(mu)otimes L^1(nu)$ as Banach spaces.
    – user10354138
    Nov 13 at 13:58













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Let $mu$ and $nu$ two measure. What is the justification to say that the measure product is a tensor product ? i.e. why $mutimes nu$ is written $muotimes nu$ ? (Of course, beside the fact that is by definition or it's just a notation). Our teacher told us that the reason that we write it as a tensor product it's because it behave as a tensor product). But I don't understand this (I'm not very confortable with tensor product).










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lovemath is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











Let $mu$ and $nu$ two measure. What is the justification to say that the measure product is a tensor product ? i.e. why $mutimes nu$ is written $muotimes nu$ ? (Of course, beside the fact that is by definition or it's just a notation). Our teacher told us that the reason that we write it as a tensor product it's because it behave as a tensor product). But I don't understand this (I'm not very confortable with tensor product).







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asked Nov 13 at 11:12









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  • For example, assuming $sigma$-finiteness, $L^1(muotimesnu)=L^1(mu)otimes L^1(nu)$ as Banach spaces.
    – user10354138
    Nov 13 at 13:58


















  • For example, assuming $sigma$-finiteness, $L^1(muotimesnu)=L^1(mu)otimes L^1(nu)$ as Banach spaces.
    – user10354138
    Nov 13 at 13:58
















For example, assuming $sigma$-finiteness, $L^1(muotimesnu)=L^1(mu)otimes L^1(nu)$ as Banach spaces.
– user10354138
Nov 13 at 13:58




For example, assuming $sigma$-finiteness, $L^1(muotimesnu)=L^1(mu)otimes L^1(nu)$ as Banach spaces.
– user10354138
Nov 13 at 13:58















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