Characterizations of Kurzweil–Henstock–Pettis integrable functions

Volume 176 / 2006

L. Di Piazza, K. Musiał Studia Mathematica 176 (2006), 159-176 MSC: Primary 26A39; Secondary 28B05, 46G10, 28A20. DOI: 10.4064/sm176-2-4


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.


  • L. Di PiazzaDepartment of Mathematics
    University of Palermo
    Via Archirafi 34
    90123 Palermo, Italy
  • K. MusiałInstitute of Mathematics
    Wrocław University
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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