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Unformatted text preview: j = 1 , 2 , . . . , the set E n,j := { x R 1 : g n ( x ) < 1 /j } is Borel measurable (why?) #4. Let A be an arbitrary nonempty set, and for each A , let an interval I := [ a , b ] be dened with 0 a < b 1. Show that there is a nite or countable subset A A , such that [ A I = [ A I . Hint. Start with a similar property for intervals I containing a xed rational point r k [0 , 1]. #5. The Cantor set (see p.38) C := n x = X j =1 a j 3 j , where a j = 0 or 2 for all j o . Find the algebraic sum C + C := { z = x + y : x, y C } . Hint. First nd 1 2 C + 1 2 C ....
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This note was uploaded on 02/15/2012 for the course MATH 8601 taught by Professor Staff during the Fall '08 term at Minnesota.
 Fall '08
 Staff
 Math

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