Approximation of lebesgue integrals by Riemann sums and lattice points in domains with fractal boundary

被引：1

作者：

Colzani, L

机构：

[1] Dipartimento di Matematica, Univ. degli Studi di Milano, 20133 Milano

来源：

MONATSHEFTE FUR MATHEMATIK | 1997年 / 123卷 / 04期

关键词：

fractals; integer points; Riemann sums;

D O I：

10.1007/BF01326765

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Sets thrown at random in space contain, on average, a number of integer points equal to the measure of these sets. We determine the mean square error in the estimate of this number when the sets are homothetic to a domain with fractal boundary. This is related to the problem of approximating Lebesgue integrals by random Riemann sums.

引用

页码：299 / 308

页数：10

共 4 条

[1] Approximation of lebesgue integrals by Riemann sums and lattice points in domains with fractal boundary
Leonardo Colzani
Monatshefte für Mathematik, 1997, 123 : 299 - 308
[2] ON RIEMANN SUMS AND LEBESGUE INTEGRALS
NAIR, R
MONATSHEFTE FUR MATHEMATIK, 1995, 120 (01): : 49 - 54
[3] Consistent first-return Riemann sums for Lebesgue integrals
Evans, MJ
Humke, PD
ACTA MATHEMATICA HUNGARICA, 2004, 103 (04) : 303 - 312
[4] Consistent first-return Riemann sums for Lebesgue integrals
Michael J. Evans
Paul D. Humke
Acta Mathematica Hungarica, 2004, 103 : 303 - 312

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