• Title/Summary/Keyword: Fatou's theorem

Search Result 7, Processing Time 0.022 seconds

A Note on Set-Valued Choquet Integrals

  • Hong, Dug-Hun;Kim, Kyung-Tae
    • Journal of the Korean Data and Information Science Society
    • /
    • v.16 no.4
    • /
    • pp.1041-1044
    • /
    • 2005
  • Recently, Zhang et al.(Fuzzy Sets and Systems 147(2004) 475-485) proved Fatou's lemma and Lebesgue dominated convergence theorem under some conditions of fuzzy measure. In this note, we show that these conditions of fuzzy measure is essential to prove Fatou's lemma and Lebesgue dominated convergence theorem by examples

  • PDF

A NOTE ON SET-VALUED FUZZY INTEGRALS

  • Hong, Dug-Hun;Kim, Kyung-Tae
    • Journal of applied mathematics & informatics
    • /
    • v.19 no.1_2
    • /
    • pp.453-456
    • /
    • 2005
  • It is known that the classical Fatou's lemma and Lebesgue convergence theorem do not require the assumption that J1. is finite. In this note, we show that the assumption $\mu$(X) < $\infty$ cannot be replaced with a weaker assumption to prove Fatou's lemma and Lebesgue convergence theorem for a sequence of set-valued measurable function suggested by Zhang and Wang (Fuzzy Sets and Systems 56(1993) 237-241).

A NEW BIHARMONIC KERNEL FOR THE UPPER HALF PLANE

  • Abkar, Ali
    • Journal of the Korean Mathematical Society
    • /
    • v.43 no.6
    • /
    • pp.1169-1181
    • /
    • 2006
  • We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

T-FUZZY INTEGRALS OF SET-VALUED MAPPINGS

  • CHO, SUNG JIN
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.4 no.1
    • /
    • pp.39-48
    • /
    • 2000
  • In this paper we define T-fuzzy integrals of set-valued mappings, which are extensions of fuzzy integrals of the single-valued functions defined by Sugeno. And we discuss their properties.

  • PDF

ON CONVERGENCE THEOREMS FOR THE MCSHANE INTEGRAL ON TIME SCALES

  • You, Xuexiao;Zhao, Dafang
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.25 no.3
    • /
    • pp.393-400
    • /
    • 2012
  • In this paper, we study the process of McShane delta integrals on time scales and discuss the relation between McShane delta integral and Henstock delta integral. We also prove the mono- tone convergence theorem, Fatou's Lemma and the dominated con- vergence theorems for the McShane delta integral.

DYNAMICAL PROPERTIES ON THE ITERATION OF CF-FUNCTIONS

  • Yoo, Seung-Jae
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.12 no.1
    • /
    • pp.1-13
    • /
    • 1999
  • The purpose of this paper is to show that if the Fatou set F(f) of a CF-meromorphic function f has two completely invariant components, then they are the only components of F(f) and that the Julia set of the entire transcendental function $E_{\lambda}(z)={\lambda}e^z$ for 0 < ${\lambda}$ < $\frac{1}{e}$ contains a Cantor bouquet by employing the Devaney and Tangerman's theorem[10].

  • PDF

On the Bayes risk of a sequential design for estimating a mean difference

  • Sangbeak Ye;Kamel Rekab
    • Communications for Statistical Applications and Methods
    • /
    • v.31 no.4
    • /
    • pp.427-440
    • /
    • 2024
  • The problem addressed is that of sequentially estimating the difference between the means of two populations with respect to the squared error loss, where each population distribution is a member of the one-parameter exponential family. A Bayesian approach is adopted in which the population means are estimated by the posterior means at each stage of the sampling process and the prior distributions are not specified but have twice continuously differentiable density functions. The main result determines an asymptotic second-order lower bound, as t → ∞, for the Bayes risk of a sequential procedure that takes M observations from the first population and t - M from the second population, where M is determined according to a sequential design, and t denotes the total number of observations sampled from both populations.