On Henstock-Dunford and Henstock-Pettis integrals.
Ye, Guoju, An, Tianqing (2001)
International Journal of Mathematics and Mathematical Sciences
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Ye, Guoju, An, Tianqing (2001)
International Journal of Mathematics and Mathematical Sciences
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José Gámez, José Mendoza (1998)
Studia Mathematica
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The two main results of this paper are the following: (a) If X is a Banach space and f : [a,b] → X is a function such that x*f is Denjoy integrable for all x* ∈ X*, then f is Denjoy-Dunford integrable, and (b) There exists a Dunford integrable function which is not Pettis integrable on any subinterval in [a,b], while belongs to for every subinterval J in [a,b]. These results provide answers to two open problems left by R. A. Gordon in [4]. Some other questions in connection with...
R. Gordon (1989)
Studia Mathematica
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Mieczysław Cichoń, Ireneusz Kubiaczyk, Sikorska-Nowak, Aneta Sikorska-Nowak, Aneta (2004)
Czechoslovak Mathematical Journal
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In this paper we prove an existence theorem for the Cauchy problem using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function satisfies some conditions expressed in terms of measures of weak noncompactness.
L. Di Piazza, K. Musiał (2006)
Studia Mathematica
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We prove that several results of Talagrand proved for the Pettis integral also hold for the Kurzweil-Henstock-Pettis integral. In particular the Kurzweil-Henstock-Pettis integrability can be characterized by cores of the functions and by properties of suitable operators defined by integrands.
C. K. Fong (2002)
Czechoslovak Mathematical Journal
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We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.