A random approach to the Lebesgue integral

被引：3
|
作者：
Grahl, Jack [1 ]
机构：
[1] UCL, Dept Math, London WC1 6BT, England
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 340卷 / 01期
关键词：
riemann integration; lebesgue integration; real function; random variable;
D O I：
10.1016/j.jmaa.2007.07.057
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct an integral of a measurable real function using randomly chosen Riemann sums and show that it converges in probability to the Lebesgue integral where this exists. We then prove some conditions for the almost sure convergence of this integral. (c) 2007 Published by Elsevier Inc.
引用
收藏
页码：358 / 365
页数：8
相关论文
共 50 条
  • [1] THE LEBESGUE INTEGRAL AS THE ALMOST SURE LIMIT OF RANDOM RIEMANN SUMS
    KIEFFER, JC
    STANOJEVIC, CV
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 85 (03) : 389 - 392
  • [2] Generalized Lebesgue integral
    Zhang, Qiang
    Mesiar, Radko
    Li, Jun
    Struk, Peter
    [J]. INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2011, 52 (03) : 427 - 443
  • [3] Centennial of the lebesgue integral
    Bony, JM
    Choquet, G
    Lebeau, G
    [J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 332 (02): : 85 - 90
  • [4] ON EXTENDING THE LEBESGUE INTEGRAL
    FORAN, J
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 81 (01) : 85 - 88
  • [5] Rethinking the Lebesgue Integral
    Lax, Peter D.
    [J]. AMERICAN MATHEMATICAL MONTHLY, 2009, 116 (10): : 863 - 881
  • [6] Expression of the Lebesgue Δ-integral on time scales as a usual Lebesgue integral;: application to the calculus of Δ-antiderivatives
    Cabada, A
    Vivero, DR
    [J]. MATHEMATICAL AND COMPUTER MODELLING, 2006, 43 (1-2) : 194 - 207
  • [7] THE CHOQUET INTEGRAL AS LEBESGUE INTEGRAL AND RELATED INEQUALITIES
    Mesiar, Radko
    Li, Jun
    Pap, Endre
    [J]. KYBERNETIKA, 2010, 46 (06) : 1098 - 1107
  • [8] KURZWEIL'S PU INTEGRAL AS THE LEBESGUE INTEGRAL
    Vyborny, Rudolf
    [J]. MATHEMATICA BOHEMICA, 2006, 131 (01): : 11 - 14
  • [9] A simplified construction of the Lebesgue integral
    V. Komornik
    [J]. Acta Mathematica Hungarica, 2019, 158 : 318 - 337
  • [10] INTEGRAL OF LEBESGUE FUNCTION OF INTERPOLATION
    ERDOS, P
    SZABADOS, J
    [J]. ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1978, 32 (1-2): : 191 - 195
12345