0000000000772423
AUTHOR
Skvortsov V.
THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL
We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.
Variational measures related to local systems and the Ward propery of P-adic path bases
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 P-adic path system that defines a differentiation basis which does not possess Ward property.