A note on choquet integrals with respect to Hausdorff capacity

1988 ◽  
pp. 115-124 ◽  
Author(s):  
David R. Adams
Keyword(s):  
Choquet Integrals ◽  
Hausdorff Capacity

scholarly journals Carleson Measure and Tent Spaces on the Siegel Upper Half Space

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Kai Zhao
Keyword(s):  
Heisenberg Group ◽  
Half Space ◽  
Carleson Measure ◽  
Atomic Decomposition ◽  
Carleson Measures ◽  
Tent Spaces ◽  
Dual Spaces ◽  
Choquet Integrals ◽  
Hausdorff Capacity

The Hausdorff capacity on the Heisenberg group is introduced. The Choquet integrals with respect to the Hausdorff capacity on the Heisenberg group are defined. Then the fractional Carleson measures on the Siegel upper half space are discussed. Some characterized results and the dual of the fractional Carleson measures on the Siegel upper half space are studied. Therefore, the tent spaces on the Siegel upper half space in terms of the Choquet integrals are introduced and investigated. The atomic decomposition and the dual spaces of the tent spaces are obtained at the last.

On a Choquet-Stieltjes type integral on intervals

2019 ◽  
Vol 69 (4) ◽  
pp. 801-814 ◽  
Author(s):  
Sorin G. Gal
Keyword(s):  
Lebesgue Measure ◽  
Choquet Integral ◽  
Stieltjes Integral ◽  
Line Integral ◽  
Type Integral ◽  
Choquet Integrals ◽  
Lebesgue Measures ◽  
Stieltjes Type

Abstract In this paper we introduce a new concept of Choquet-Stieltjes integral of f with respect to g on intervals, as a limit of Choquet integrals with respect to a capacity μ. For g(t) = t, one reduces to the usual Choquet integral and unlike the old known concept of Choquet-Stieltjes integral, for μ the Lebesgue measure, one reduces to the usual Riemann-Stieltjes integral. In the case of distorted Lebesgue measures, several properties of this new integral are obtained. As an application, the concept of Choquet line integral of second kind is introduced and some of its properties are obtained.

Fuzzy Measures and Choquet Integrals based on Fuzzy Covering Rough Sets

2021 ◽  
pp. 1-1
Author(s):  
Xiaohong Zhang ◽  
Jingqian Wang ◽  
Jianming Zhan ◽  
Jianhua Dai
Keyword(s):  
Rough Sets ◽  
Fuzzy Measures ◽  
Choquet Integrals

scholarly journals Indicators for the characterization of discrete Choquet integrals

2014 ◽  
Vol 267 ◽  
pp. 201-216 ◽  
Author(s):  
Jaume Belles-Sampera ◽  
José M. Merigó ◽  
Montserrat Guillén ◽  
Miguel Santolino
Keyword(s):  
Choquet Integrals

scholarly journals Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation

2006 ◽  
Vol 207 (2) ◽  
pp. 828-846 ◽  
Author(s):  
Jie Xiao
Keyword(s):  
Heat Equation ◽  
Besov Space ◽  
Hausdorff Capacity

Aggregation of Choquet Integrals

2016 ◽  
pp. 58-64
Author(s):  
Radko Mesiar ◽  
Ladislav Šipeky ◽  
Alexandra Šipošová
Keyword(s):  
Choquet Integrals

scholarly journals On the moments and distribution of discrete Choquet integrals from continuous distributions

2009 ◽  
Vol 230 (1) ◽  
pp. 83-94
Author(s):  
Ivan Kojadinovic ◽  
Jean-Luc Marichal
Keyword(s):  
Continuous Distributions ◽  
Choquet Integrals

Choquet integrals of weighted intuitionistic fuzzy information

2010 ◽  
Vol 180 (5) ◽  
pp. 726-736 ◽  
Author(s):  
Zeshui Xu
Keyword(s):  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Choquet Integrals
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