A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals

被引：2

作者：

Fong, CK ^{[1
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ottawa, ON K1S 5B6, Canada

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2002年 / 52卷 / 03期

关键词：

Pettis integrability; HK-integrals; Saks-Henstock's property;

D O I：

10.1023/A:1021719627933

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：531 / 536

页数：6

共 35 条

[1] A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals
C. K. Fong
Czechoslovak Mathematical Journal, 2002, 52 : 531 - 536
[2] The New Extensions of the Henstock-Kurzweil and the McShane Integrals of Vector-Valued Functions
Kaliaj, Sokol Bush
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (01)
[3] Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions
Naralenkov, Kirill
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2011, 61 (04) : 1091 - 1106
[4] Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions
Kirill Naralenkov
Czechoslovak Mathematical Journal, 2011, 61 : 1091 - 1106
[5] A bilinear version of Orlicz-Pettis theorem
Blasco, O.
Calabuig, J. M.
Signes, T.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 348 (01) : 150 - 164
[6] Description of the limit set of Henstock-Kurzweil integral sums of vector-valued functions
Caponetti, D.
Di Piazza, L.
Kadets, V.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 421 (02) : 1151 - 1162
[7] Convergence and Comparison Results for Henstock-Kurzweil and McShane Integrable Vector-Valued Functions
Heikkila, S.
Ye, Guoju
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2011, 35 (03) : 407 - 418
[8] The New Extensions of the Henstock–Kurzweil and the McShane Integrals of Vector-Valued Functions
Sokol Bush Kaliaj
Mediterranean Journal of Mathematics, 2018, 15
[9] A Henstock-Kurzweil integrable vector-valued function which is not McShane integrable on any portion
Naralenkov, K. M.
QUAESTIONES MATHEMATICAE, 2012, 35 (01) : 11 - 21
[10] ON KURZWEIL-HENSTOCK-PETTIS AND KURZWEIL-HENSTOCK INTEGRALS OF BANACH SPACE-VALUED FUNCTIONS
Ye Guoju
TAIWANESE JOURNAL OF MATHEMATICS, 2010, 14 (01): : 213 - 222

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