Suppose that f:[a,b] --> R is of bounded variation on every closed subinterval of (a,b). Does it follow that f is of bounded variation on [a,b]?

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- October 4th 2009, 11:56 AMqwe123Question about bounded variation
Suppose that f:[a,b] --> R is of bounded variation on every closed subinterval of (a,b). Does it follow that f is of bounded variation on [a,b]?

- November 14th 2010, 12:51 PMRebesques
If a discontinuous function on [0,1] has, say, finite length on every closed subinterval of (0,1),

does it necessarily have finite length over [0,1]?