# Question: a If M is a k dimensional manifold

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.

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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