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  3. 1 let s c r define the quotinner measure of...

Question: 1 let s c r define the quotinner measure of...

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1 Let S C R. Define the inner measure of S by: m.(S) supm*(K) KSS, K-compact) (a) Show that if S is a bounded set in R, and I is a bounded interval containing S, then m.(S) (I) m(IS, where (I) is the length of the interval I Note: this does not depend on the choice of I; compare to Example 16.3(f) in Carothers text... (b) Clearly, m.(E m(E) in e In the case E is a bounded subset of R such that m.(E(E), prove that for any FCR mr(F \ E) + ml. (F n E) = m. (F).
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