The Kurzweil integral with exclusion of negligible sets
نویسندگان
چکیده
منابع مشابه
The Kurzweil Integral with Exclusion of Negligible Sets
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of δ-fine partitions by excluding small sets.
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We apply the Kurzweil-Henstock integral setting to prove a Fredholm Alternative-type result for the integral equation x (t)− K Z [a,b] α (t, s)x (s) ds = f (t) , t ∈ [a, b] , where x and f are Kurzweil integrable functions (possibly highly oscillating) defined on a compact interval [a, b] of the real line with values on Banach spaces. An application is given.
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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.
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2003
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2003.134183