Let the function f be absolutely continuous on [a, b]. Prove: (i) If f is Liptschitz...

    

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Let the function f be absolutely continuous on [a, b]. Prove: (i) If f is Liptschitz on [a, b], then there is a constant M> 0 such that f'| ≤ M a.e. on [a, b]. (ii) If there is a constant M >0 such that f'M a.e. on [a, b], then f is Liptschitz on [a, b]. Let the function f be absolutely continuous on [a, b]. Prove: (i) If f is Liptschitz on [a, b], then there is a constant M> 0 such that f'| ≤ M a.e. on [a, b]. (ii) If there is a constant M >0 such that f'M a.e. on [a, b], then f is Liptschitz on [a, b].

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