Generalized Fuzzy Measurability

  • Anca CroitoruEmail author
  • Nikos Mastorakis
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 343)


In this paper we introduce two concepts of generalized measurability for set-valued functions, namely \(\varphi\)-μ-total-measurability and \(\varphi\)-μ-measurability relative to a non-negative function \(\varphi: \mathcal{P}_{0}(X) \times \mathcal{P}_{0}(X) \rightarrow [0,+\infty )\) and a non-negative set function \(\mu: \mathcal{A}\rightarrow [0,+\infty )\) and present some relationships between them. We also define different types of convergences for sequences of set-valued functions and prove some relationships among them and a theorem of Egorov type. Finally, we introduce two semi-metrics on a space of set-valued functions and then compare them.


Measurable Totally-measurable Set-valued function Theorem of Egorov type Almost everywhere convergent Pseudo-almost everywhere convergent Almost uniformly convergent Pseudo-almost uniformly convergent 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics“Al. I. Cuza” UniversityIaşiRomania
  2. 2.Technical University of SofiaSofiaBulgaria

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