MATH 3220 § 1	ELEVENTH HOMEWORK ASSIGNMENT	Nov. 28, 2000
A. Treibergs		Due Dec. 5, 2000

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• Please hand in the following exercises from the text "Introduction to Analysis, Second Edition" by William Wade, Prentice Hall 1999.
• 380[ 2, 4a, 7ab, 10 ].

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• Here are the equivalent exercises for those using the First Edition:
• 346[ 4a, 10 ]
• 1. Prove that every finite subset of Rⁿ is a Jordan region of volume zero.
  2. Show that even in R², part a. is not true if "finite" is replaced by "countable."
  3. By an interval in R² we mean a set of the form for some real a, b, c. Prove that every interval in R² is a Jordan region.
• Suppose that V is a bounded open set of Rⁿ and g:V -> Rⁿ is continuously differentiable on V.
  1. Let H be a compact subset of V. Show that there is a constant C>0 (depending only on g, H, n) so that for all cubes Q in H,

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  2. Show that if E, a subset of V has volume zero then g(E) has volume zero.