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Start Over Creator Kurzweil, Jaroslav

1. A nonexistence result for the Kurzweil integral

Creator:
Krejčí, Pavel and Kurzweil, Jaroslav
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Kurzweil integral and regulated functions
Language:
English
Description:
It is shown that there exist a continuous function f and a regulated function g defined on the interval [0,1] such that g vanishes everywhere except for a countable set, and the K *-integral of f with respect to g does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. McShane equi-integrability and Vitali’s convergence theorem

Creator:
Kurzweil, Jaroslav and Schwabik, Štefan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
McShane integral, Vitali convergence theorem, and equi-integrability
Language:
English
Description:
The McShane integral of functions f : I → ! defined on an m-dimensional interval I is considered in the paper. This integral is known to be equivalent to the Lebesgue integral for which the Vitali convergence theorem holds. For McShane integrable sequences of functions a convergence theorem based on the concept of equi-integrability is proved and it is shown that this theorem is equivalent to the Vitali convergence theorem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public