Question: If M is an -dimensional manifold in Rn, with the usual orientation, show that dV = dx1^ . . . ^ dxn, so that the

If M is an -dimensional manifold in Rn, with the usual orientation, show that dV = dx1^ . . . ^ dxn, so that the volume of M, as defined in this section, is the volume as defined in Chapter 3. (Note that this depends on the numerical factor in the definition of w ^ n.)

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