<p style='text-indent:20px;'>Some limit theorems are presented for Riemann-Lebesgue integrals where the functions <inline-formula><tex-math id="M1">\begin{document}$ G_n $\end{document}</tex-math></inline-formula> and measures id="M2">\begin{document}$ M_n interval valued convergence multisubmeasures is setwise. In particular sufficient conditions in order to ob...

Let f be a distribution (generalised function) on the real line. If there is a continuous function F with real limits at infinity such that F ′ = f (distributional derivative) then the distributional integral of f is defined as ∫ ∞ −∞ f = F (∞)−F (−∞). It is shown that this simple definition gives an integral that includes the Lebesgue and Henstock–Kurzweil integrals. The Alexiewicz norm leads ...

In this paper, I provide the basis for a measureand integral-theoretic formulation of possibility theory. It is shown that, using a general definition of possibility measures, and a generalization of Sugeno’s fuzzy integral – the seminormed fuzzy integral, or possibility integral –, a unified and consistent account can be given of many of the possibilistic results extant in the literature. The ...

where s is a “type parameter”, usually s = −i or s = 1, s = −i standing for “oscillatory”, s = 1 for “probabilistic type”. Φ is a real-valued function, in the probabilistic case assumed to be lower bounded; it is called “phase function”; f is a complex-valued function, called “amplitude function”; γ is thought to be a member of some space Γ “on which the integration extends”; dγ is a heuristic ...

In this contribution we define a new class of non-linear integrals based on decomposition integrals. These integrals are motivated by greediness of many real-life situations. Another view on this new class of integrals is that it is a generalization of both the Shilkret and PAN integrals. Moreover, it can be seen as an iterated Shilkret integral. Also, an example in time-series analysis is prov...

We introduce a new operation between nonnegative integrable functions on R n $\mathbb {R}^n$ , that we call geometric combination; it is obtained via mass transportation approach, playing with inverse distribution functions. The main feature of this the Lebesgue integral combination equals mean two separate integrals; as natural consequence, derive functional inequality Prékopa–Leindler type. W...

Weighted inequalities with power-type weights for operators of harmonic analysis, such as maximal and singular integral operators, commutators integrals in grand variable exponent Lebesgue spaces are derived. The defined on quasi-metric measure doubling condition (spaces homogeneous type). proof the result regarding Hardy–Littlewood operator is based appropriate sharp weighted norm estimates we...

In a previous paper, we obtained several “compact versions” of Rubio de Francia’s weighted extrapolation theorem, which allowed us to extrapolate the compactness linear operators from just one space full range Lebesgue spaces, where these are bounded. this study for bilinear in terms Muckenhoupt weights. As applications, easily recover and improve earlier results on commutators Calderón–Zygmund...

The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. generalisation that we replace exponential function with Mittag-Leffler-type function, oscillatory integrals appearing in analysis time-fractional partial differential equations. More specifically, integral form I?,?(?)=?RE?,?(i???(x))?(x)dx, for range 00. This extends variety estimat...