Prove that R = [a1, b1] x..x [an, bn] is not of content if ai < bi for i =1. n.
Answer to relevant Questionsa. Show that an unbounded set cannot have content 0.Show that if f, g: A → R are integrable, so is f ∙ g.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.If A = [a1, b1] x . x [an, bn] and f: A → R is continuous, define f: A → R byIf M is a k-dimensional manifold with boundary, prove that ∂M is a (k - 1) -dimensional manifold and M - ∂M is a k=dimensional manifold.
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