PreprintCC BY 4.0arXiv
A Radon-Nikodým theorem for Fuzzy Number Multimeasures in Locally Convex Spaces
Abstract
In this paper, we present a Radon-Nikodym theorem for dominated fuzzy number multimeasures defined on Σ and taking values in ℱcwk(X), where $(Ω, Σ, μ)$ is a complete finite measure space and ℱcwk(X) is the family of generalized fuzzy numbers on a Hausdorff locally convex topological vector space X, i.e., a map u: X → [0,1] is a member of ℱcwk(X), if and only if for each α∈ (0,1] the α-cut [u]α of u is a member of the family cwk(X) of all nonempty convex and weakly compact subsets of X, ([u]α = {x ∈ X: u(x) ≥ α}).
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BibTeX
@misc{kaliaj2026radonnikodým,
title = {{A Radon-Nikodým theorem for Fuzzy Number Multimeasures in Locally Convex Spaces}},
author = {Sokol Kaliaj},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35883},
eprint = {2610.35883},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35883},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Radon-Nikodým theorem for Fuzzy Number Multimeasures in Locally Convex Spaces
AU - Sokol Kaliaj
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.35883
UR - https://arxiv.org/abs/2610.35883
AB - In this paper, we present a Radon-Nikodym theorem for dominated fuzzy number multimeasures defined on Σ and taking values in ℱ_cwk(X), where $(Ω, Σ, μ)$ is a complete finite measure space and ℱ_cwk(X) is the family of generalized fuzzy numbers on a Hausdorff locally convex topological vector space X, i.e., a map u: X → [0,1] is a member of ℱ_cwk(X), if and only if for each α∈ (0,1] the α-cut [u]^α of u is a member of the family cwk(X) of all nonempty convex and weakly compact subsets of X, ([u]^α = {x ∈ X: u(x) ≥ α}).
ER -