Show that if C has content 0, then C C A for some closed rectangle A and C is Jordan-measurable and ∫ AXC = 0.
Answer to relevant QuestionsGive an example of a bounded set C of measure 0 such that ∫ AXC does not exist.If A is a Jordan measurable set and ε > 0, show that there is a compact Jordan measurable set C C A such that ∫ A − C1 < ε.Use Fubini's Theorem to derive an expression for the volume of a set in R3 obtained by revolving a Jordan measurable set in the yz -plane about the -axis.Use Theorem 3-14 to prove Theorem 3-13 without the assumption that g1 (x) ≠ 0.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 ...
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