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(3) Let S be a bounded subset of R2. Define the outer Jordan content of S to be n т J*(S) = inf{ \Sel : SSU Se is a cove
Posted: Mon May 02, 2022 4:26 pm
by answerhappygod
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(3) Let S be a bounded subset of R2. Define the outer Jordan content of S to be n т J*(S) = inf{ \Sel : SSU Se is a covering of S by finitely many open rectangles } k=1 k=1 You may use without proof the fact that the definition is unchanged if we use closed rect- angles instead of open ones (as in the previous problem). (a) Prove that this is equal to the upper Riemann integral of the indicator function, U(xs). (b) Prove that J*(S) = J*(S). (c) Clearly m*(S) < J*(S). Give an example that shows the inequality can be strict. т