Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.
Stepanoff's theorem is extended to infinitely dimensional separable Banach spaces.
Some properties of absolutely continuous variational measures associated with local systems of sets are established. The classes of functions generating such measures are described. It is shown by constructing an example that there exists a -adic path system that defines a differentiation basis which does not possess Ward property.
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.
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