Things that do not depend on the choice of Cauchy surface

naima
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A Cauchy surface is a 3d spacelike slice of spacetime.
Could you read the definition (17) p18
the author says that "one can proove that ##\sigma## does not depend on the choice of the Cauchy surface because the functions obey the law of motion."
Could you elaborate?
Thanks

Could anyone add "h" in the title (choice)?
 
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I found the proof several lines below!
 

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