Let E be a nonempty subset of R. Find an open set U of R that satisfies the following two conditions: E C U and m*(U) ≤m*(E) + ¼ [20 marks]
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Originally Posted by cynthiacheok Let E be a nonempty subset of R. Find an open set U of R that satisfies the following two conditions: E C U and m*(U) ≤m*(E) + ¼ [20 marks] The usual definition of outer measure m* is: , where the infimum is taken over all countable collections of open intervals such that . That means that we can find such a countable collection satisfying . Define . Then E ⊆ U. Also, and so .
Last edited by Opalg; Aug 23rd 2008 at 12:44 AM.
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