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 16 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 the approximation of lebesgue integrals by Riemann sums
Jessen, B
ANNALS OF MATHEMATICS, 1934, 35 : 248 - 251
[3] RIEMANN SUMS AND LEBESGUE INTEGRALS
BAKER, RC
QUARTERLY JOURNAL OF MATHEMATICS, 1976, 27 (106): : 191 - 198
[4] ON RIEMANN SUMS AND LEBESGUE INTEGRALS
NAIR, R
MONATSHEFTE FUR MATHEMATIK, 1995, 120 (01): : 49 - 54
[5] ON APPROXIMATING LEBESGUE INTEGRALS BY RIEMANN SUMS
REVESZ, SG
RUZSA, IZ
GLASGOW MATHEMATICAL JOURNAL, 1991, 33 : 129 - 134
[6] Consistent first-return Riemann sums for Lebesgue integrals
Evans, MJ
Humke, PD
ACTA MATHEMATICA HUNGARICA, 2004, 103 (04) : 303 - 312
[7] Consistent first-return Riemann sums for Lebesgue integrals
Michael J. Evans
Paul D. Humke
Acta Mathematica Hungarica, 2004, 103 : 303 - 312
[8] Discrete fractional integrals, lattice points on short arcs, and diophantine approximation
Temur, Faruk
TURKISH JOURNAL OF MATHEMATICS, 2022, 46 (07) : 2867 - 2889
[9] Approximation of Riemann-Liouville Type Integrals on an Interval by Methods Based on Fourier-Chebyshev Sums
Potseiko, P. G.
Rovba, E. A.
MATHEMATICAL NOTES, 2024, 116 (1-2) : 104 - 118
[10] The Riemann boundary value problem in the class of Cauchy type integrals with densities of grand variable exponent Lebesgue spaces
Kokilashvili, Vakhtang
Meskhi, Alexander
Paatashvili, Vakhtang
GEORGIAN MATHEMATICAL JOURNAL, 2016, 23 (04) : 551 - 558

← 1 2 →