Sentence examples for measures and integrals from inspiring English sources
It is well known that the latter plays a crucial role in the construction of explicit bounds to probability measures and integrals given a fixed number of moments.
Román-Flores et al. [7 11] studied the level-continuity of fuzzy integrals, H-continuity of fuzzy measures and geometric inequalities for fuzzy measures and integrals, respectively.
We shall denote | g | ( O ) : = ∫ O | g | d x ~ therefore adopting a unified notation for both measures and integrals of L 1 -maps.
where the supremum is over all balls B ⊂ E. Since then, the weight functions have been well studied and widely used in analysis and PDEs, particularly in areas of the measures and integrals, see [2 11].
Triangular norms based on a notion used by Menger [1] were introduced by Schweizer and Sklar [2] in the framework of probabilistic metric spaces, and they play a fundamental role in several branches of mathematics like in fuzzy logics and their applications [3, 4], the games theory [5], the non-additive measures and integral theory [6 8].
The following result, expressed by the measure and integral, is the most commonly used.
For basic properties of the integrals of vector-valued functions with respect to scalar measures and the integrals of scalar-valued functions with respect to vector measures, see Chapter II in [12].
Fuzzy measures and fuzzy integrals have been successfully used in many real applications.
The properties and applications of the fuzzy measures and fuzzy integrals have been studied by many authors.
The proposed model fuzzifies the forward and backward variables by incorporating Sugeno fuzzy measures and Choquet integrals, thus further extends the generalized HMM.
