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On indefinite BV-integrals

Donatella Bongiorno, Udayan B. Darji, Washek Frank Pfeffer (2000)

Commentationes Mathematicae Universitatis Carolinae

We present an example of a locally BV-integrable function in the real line whose indefinite integral is not the sum of a locally absolutely continuous function and a function that is Lipschitz at all but countably many points.

On integrability in F-spaces

Mikhail Popov (1994)

Studia Mathematica

Some usual and unusual properties of the Riemann integral for functions x : [a,b] → X where X is an F-space are investigated. In particular, a continuous integrable l p -valued function (0 < p < 1) with non-differentiable integral function is constructed. For some class of quasi-Banach spaces X it is proved that the set of all X-valued functions with zero derivative is dense in the space of all continuous functions, and for any two continuous functions x and y there is a sequence of differentiable...

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