<abstract xmlns="http://www.w3.org/1999/xhtml">Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_udt-2020-0013_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>μ</mi></mrow><mi>C</mi></msub><mo>↦</mo><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mrow><msub><mrow><mrow><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mrow><mi>F</mi><mi>d</mi></mrow></mrow></mrow></mrow><mi>μ</mi></msub><msub><mrow></mrow><mi>C</mi></msub><mo>,</mo></mrow></mrow></mrow></math><tex-math>{\mu _C} \mapsto \int_0^1 {{{\int_0^1 {Fd} }_\mu }_C,}</tex-math></alternatives></disp-formula>
where <italic>µC</italic> is a copula measure and <italic>F</italic> is a Riemann integrable function on [0, 1]2 of a specific type. Such problems have been considered in [4] and are of interest in the study of limit points of two uniformly distributed sequences.</abstract>

Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type
μC↦∫01∫01FdμC,{\mu _C} \mapsto \int_0^1 {{{\int_0^1 {Fd} }_\mu }_C,}
where µC is a copula measure and F is a Riemann integrable function on [0, 1]2 of a specific type. Such problems have been considered in [4] and are of interest in the study of limit points of two uniformly distributed sequences.

On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

Dipartimento di Matematica e Fisica “Ennio De Giorgi”

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Motivated by the maximal average distance of uniformly distributed sequences we consider some extremal problems for functionals of type
μC↦∫01∫01FdμC,{\mu _C}...

On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

Published Online: Dec 25, 2020

Page range: 99 - 112

Received: Jun 12, 2020

Accepted: Nov 15, 2020

DOI: https://doi.org/10.2478/udt-2020-0013

Keywords
Uniform distribution, Copulas, Extremal problems

© 2020 Fabrizio Durante et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On Extremal Problems for Pairs of Uniformly Distributed Sequences and Integrals with Respect to Copula Measures

Published Online: Dec 25, 2020

Page range: 99 - 112

Received: Jun 12, 2020

Accepted: Nov 15, 2020

DOI: https://doi.org/10.2478/udt-2020-0013

KeywordsUniform distribution, Copulas, Extremal problems

© 2020 Fabrizio Durante et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Uniform distribution, Copulas, Extremal problems