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Posted: **Wed May 11, 2022 9:29 pm**

: 6 Prove That A Function F 0 1 R Is Absolutely Continuous On 0 1 If And Only If There Exists A Sequence Fn Of L 1 (48.55 KiB) Viewed 22 times

6 Prove that a function f : [0, 1] → R is absolutely continuous on [0, 1] if and only if there exists a sequence fn of Lipschitz functions on [0, 1] so that V(fn – f;0,1) + 0 as n + 00. (Here V(h;0, 1) denotes the total variation of a function h over the interval [0.1]) a