An Application of the Choquet Theorem to the Study of Randomly-superinvariant Measures
نویسنده
چکیده
Given a real valued random variable Θ we consider Borel measures μ on B(R), which satisfy the inequality μ(B) ≥ Eμ(B−Θ) (B ∈ B(R)) (or the integral inequality μ(B) ≥ R∞ −∞ μ(B−h)γ(dh)). We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable Θ.
منابع مشابه
An extension theorem for finite positive measures on surfaces of finite dimensional unit balls in Hilbert spaces
A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...
متن کاملConstruction of measures of noncompactness of $C^k(Omega)$ and $C^k_0$ and their application to functional integral-differential equations
In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these spaces. Finally, as an application, we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixe...
متن کاملThe 2-additive fuzzy Choquet integral-based TODIM method with improved score function under hesitant fuzzy environment
Recently, the TODIM$^1$(an acronym in Portuguese of interactive and multi-criteria decision making) method has attracted increasing attention and many researchers have extended it to deal with multiple attribute decision making (MADM) problems under different situations. However, none of them can be used to handle MADM problems with positive, independent, and negative interactions among attribu...
متن کاملApplication of measures of noncompactness to infinite system of linear equations in sequence spaces
G. Darbo [Rend. Sem. Math. Univ. Padova, 24 (1955) 84--92] used the measure of noncompactness to investigate operators whose properties can be characterized as being intermediate between those of contraction and compact operators. In this paper, we apply the Darbo's fixed point theorem for solving infinite system of linear equations in some sequence spaces.
متن کاملGeneralization of Darbo's fixed point theorem and application
In this paper, an attempt is made to present an extension of Darbo's theorem, and its applicationto study the solvability of a functional integral equation of Volterra type.
متن کامل