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6) If E is any countable subset of real numbers prove that A*(E) = A*(E) = 0. 7) Show that the se...

6) If E is any countable subset of real numbers prove that A*(E) = A*(E) = 0. 7) Show that the set of all real numbers IR is measurable with >(IR) = . 8) Prove that If f : [a, b] IR is continuous [a; b]then it is measurable [a, b]. 9) Give an example of a function f : [O, 1] IR which is measurable on [O, 1] but not continuos on [O, 1]. 10) Find the Lebesgue integral of the following functions a) f : [O, 1] IR defined by f(x) = O if x is rational and f(x) = 2 if x is irrational. b) f : [O, 1] --- IR defined by f(x) = x2 for all x E [O, 1]

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OR よ Lo ark ntegratim거)二 9)

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