Generalization of inclusion–exclusion integral for nondiscrete monotone measure space

2019 ◽  
Vol 355 ◽  
pp. 42-58 ◽  
Author(s):  
Aoi Honda ◽  
Yoshiaki Okazaki
Keyword(s):  
Measure Space ◽  
Monotone Measure

On the Integrability of the Ergodic Hilbert Transform for A Class of Functions with Equal Absolute Values

1998 ◽  
Vol 5 (2) ◽  
pp. 101-106
Author(s):  
L. Ephremidze
Keyword(s):  
Hilbert Transform ◽  
Measure Space ◽  
Integrable Function ◽  
Finite Measure ◽  
Ergodic Transformation ◽  
Finite Measure Space ◽  
Class Of Functions

Abstract It is proved that for an arbitrary non-atomic finite measure space with a measure-preserving ergodic transformation there exists an integrable function f such that the ergodic Hilbert transform of any function equal in absolute values to f is non-integrable.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

scholarly journals Fairness and fuzzy coalitions

2021 ◽  
Author(s):  
Chiara Donnini ◽  
Marialaura Pesce
Keyword(s):  
New York ◽  
Economic Theory ◽  
Measure Space ◽  
Exchange Economy ◽  
Mathematical Methods ◽  
Competitive Equilibria ◽  
Fuzzy Coalitions ◽  
Core Allocations

AbstractIn this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

scholarly journals Geometry and dynamics of admissible metrics in measure spaces

2013 ◽  
Vol 11 (3) ◽  
Author(s):  
Anatoly Vershik ◽  
Pavel Zatitskiy ◽  
Fedor Petrov
Keyword(s):  
Invariant Measure ◽  
Wide Class ◽  
Lebesgue Space ◽  
Measure Space ◽  
Asymptotic Properties ◽  
Ergodic Transformation ◽  
Measure Spaces ◽  
Admissible Metric ◽  
Discreteness Criterion ◽  
Uniformly Bounded

AbstractWe study a wide class of metrics in a Lebesgue space, namely the class of so-called admissible metrics. We consider the cone of admissible metrics, introduce a special norm in it, prove compactness criteria, define the ɛ-entropy of a measure space with an admissible metric, etc. These notions and related results are applied to the theory of transformations with invariant measure; namely, we study the asymptotic properties of orbits in the cone of admissible metrics with respect to a given transformation or a group of transformations. The main result of this paper is a new discreteness criterion for the spectrum of an ergodic transformation: we prove that the spectrum is discrete if and only if the ɛ-entropy of the averages of some (and hence any) admissible metric over its trajectory is uniformly bounded.

Endpoint estimates of positive operators in a filtered measure space

2017 ◽  
Vol 109 (5) ◽  
pp. 477-488
Author(s):  
Yahui Zuo ◽  
Lian Wu ◽  
Yong Jiao
Keyword(s):  
Measure Space ◽  
Positive Operators
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