Geodesic
APPROXIMATION OF BANACH SPACE VALUED NON-ABSOLUTELY INTEGRABLE FUNCTIONS BY STEP FUNCTIONS
Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 583-593

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DOI

The approximation of Banach space valued non-absolutely integrable functions by step functions is studied. It is proved that a Henstock integrable function can be approximated by a sequence of step functions in the Alexiewicz norm, while a Henstock–Kurzweil–Pettis and a Denjoy–Khintchine–Pettis integrable function can be only scalarly approximated in the Alexiewicz norm by a sequence of step functions. In case of Henstock–Kurzweil–Pettis and Denjoy–Khintchine–Pettis integrals the full approximation can be done if and only if the range of the integral is norm relatively compact.
DOI : 10.1017/S0017089508004448
Mots-clés : Primary 28B20, Secondary 26A39, 28B05, 46G10, 54C60 
BONGIORNO, B.; PIAZZA, L. DI; MUSIAŁ, K. APPROXIMATION OF BANACH SPACE VALUED NON-ABSOLUTELY INTEGRABLE FUNCTIONS BY STEP FUNCTIONS. Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 583-593. doi: 10.1017/S0017089508004448
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     title = {APPROXIMATION {OF} {BANACH} {SPACE} {VALUED} {NON-ABSOLUTELY} {INTEGRABLE} {FUNCTIONS} {BY} {STEP} {FUNCTIONS}},
     journal = {Glasgow mathematical journal},
     pages = {583--593},
     year = {2008},
     volume = {50},
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     doi = {10.1017/S0017089508004448},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004448/}
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