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I am studying Sean Carroll's "Lecture notes on General Relativity". In the second chapter he identifies the volume element [itex]d^nx[/itex] on an n-dimensional manifold with

[tex]

dx^0\wedge\ldots\wedge dx^{n-1}.

[/tex]

He then claims that this wedge product should be interpreted as a coordinate dependent object (he also proves that this object is in fact a tensor density). But, looking from an other point of view, if [itex]dx^\mu[/itex] is a well defined one-form, then how can the wedge product of these one-forms be a coordinate dependent object instead of being a well defined n-form?

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# Tensor density from wedge product

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