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Problem 5. Let f be absolutely continuous in the interval [ε, 1] for each 0 <...

Problem 5. Let f be absolutely continuous in the interval [ε, 1] for each 0 < ε < 1. Does the continuity off f at 0 imply that f is absolutely continuous on [0, 1] ? What if f is also of bounded variation on [0, 1]?

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