Autocontinuity, convergence in measure, and convergence in distribution
References (4)
The autocontinuity of set function and fuzzy integral
J. Math. Anal. Appl.
(1984)Non-Additive Measure and Integral
(1994)
Cited by (19)
A universal, canonical dispersive ordering in metric spaces
2021, Journal of Statistical Planning and InferenceThe Vitali convergence in measure theorem of nonlinear integrals
2020, Fuzzy Sets and SystemsCitation Excerpt :A nonadditive measure is a monotone set function vanishing at the empty set and yields several types of nonlinear integrals such as the Choquet [2,21], Šipoš [24], Sugeno [19,26], and Shilkret [23,33] integrals. For those nonlinear integrals, depending on a variety of modes of convergence of functions, various types of convergence theorems have been discussed; see [3,4,8–13,17–20,24,25,28–30,33] and others. In previous papers [9,11,12], the monotone convergence theorem, the Fatou lemma, the bounded convergence theorem, and the dominated convergence theorem of nonlinear integrals were investigated in terms of pointwise convergence of functions.
A note on the pseudo Stolarsky type inequality for the g¯ -integral
2015, Applied Mathematics and ComputationCitation Excerpt :Pap and Stajner [13] introduced the generalized pseudo-convolution of functions and their properties. Aumann [1], Deschrijver [4], Grabisch [8], Ha and Wu [9], Murofushi et al. [12], and Wechselberger [16] have been studying various integrals of measurable interval-valued functions which are used for representing uncertain functions, for examples, the Aumann integral the fuzzy integral of measurable interval-valued functions in many different mathematical theories and their applications. Recently, Daraby [3] proved the Stolarsky type inequality for pseudo-integrals and Jang [10] defined the interval-valued generalized with respect to a fuzzy measure by using interval-representable pseudo-operations of measurable interval-valued functions and investigated their properties.
The bounded convergence in measure theorem for nonlinear integral functionals
2015, Fuzzy Sets and SystemsCitation Excerpt :In Section 5, we present conclusions. The following notions of essential boundedness of functions are already discussed in [2, p. 105] and [7, Definition 3.2]. This can be proved directly from Definition 2.1.
Metrizability of the Lévy topology on the space of nonadditive measures on metric spaces
2012, Fuzzy Sets and Systems