# Question: Give an example of a bounded set C

Give an example of a bounded set C of measure 0 such that ∫ AXC does not exist.

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If C is a bounded set of measure 0 and ∫ AXC exists, show that ∫ AXC = 0.Let C C A x B be a set of content 0. Let A1 C A be the set of all x Є A such that {y Є B: (x, y) Є C} is not of content 0. Show that A1 is a set of measure 0.If A = [a1, b1] x . x [an, bn] and f: A → R is continuous, define f: A → R byIf g: Rn → Rn and detg1 (x) ≠ 0, prove that in some open set containing we can write g = to gn 0 ∙ ∙ ∙ o g1, 0.., where is of the form gi(x) = (x1, ∙ ∙ ∙ Fi (x) , ∙ ...Show that Mx consists of the tangent vectors at t of curves in M with c (t) = x.Post your question