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Further results on laws of large numbers for uncertain random variables

Feng Hu, Xiaoting Fu, Ziyi Qu, Zhaojun Zong (2023)

Kybernetika

The uncertainty theory was founded by Baoding Liu to characterize uncertainty information represented by humans. Basing on uncertainty theory, Yuhan Liu created chance theory to describe the complex phenomenon, in which human uncertainty and random phenomenon coexist. In this paper, our aim is to derive some laws of large numbers (LLNs) for uncertain random variables. The first theorem proved the Etemadi type LLN for uncertain random variables being functions of pairwise independent and identically...

Generalized Hermitean ultradistributions

C. Andrade, L. Loura (2009)

Mathematica Bohemica

In this paper we define, by duality methods, a space of ultradistributions ω ' ( ℝ N ) . This space contains all tempered distributions and is closed under derivatives, complex translations and Fourier transform. Moreover, it contains some multipole series and all entire functions of order less than two. The method used to construct 𝔾 ω ' ( ℝ N ) led us to a detailed study, presented at the beginning of the paper, of the duals of infinite dimensional locally convex spaces that are inductive limits of finite dimensional...

Generalized precompactness and mixed topologies.

Jurie Conradie (1993)

Collectanea Mathematica

The equicontinuous sets of locally convex generalized inducted limit (or mixed) topologies are characterized as generalized precompact sets. Uniformly pre-Lebesgue and Lebesgue topologies in normed Riesz spaces are investigated and it is shown that order precompactness and mixed topologies can be used to great advantage in the study of these topologies.

Generalized-lush spaces and the Mazur-Ulam property

Dongni Tan, Xujian Huang, Rui Liu (2013)

Studia Mathematica

We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (in particular, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We find that the space C(K,E) of vector-valued continuous functions is a GL-space whenever E is, and show that the set of GL-spaces is stable under c₀-, l₁- and l ∞ -sums. As an application, we prove that the Mazur-Ulam property holds for a larger...

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