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a. If M is a k-dimensional manifold in Rn and k < n, show that M has measure 0.
b. If M is a closed -dimensional manifold with boundary in Rn, show that the boundary of M is ∂M. Give a counter-example if M is not closed.
c. If M is a compact -dimensional manifold with boundary in Rn, show that M is Jordan-measurable. |
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