A convolution inequality concerning Cantor-Lebesgue measures.
A Daniell integral approach to nonstandard Kurzweil-Henstock integral
A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results.
A derivative to match the v-integral.
A discrete version of an open problem and several answers.
A game of fair division with continuum of players
A general rearrangement inequality à la Hardy-Littlewood.
A linear Radon-Nikodym type theorem for -algebras with applications to measure theory
A note on Riemann integrability.
A PU-integral on an abstract metric space
In this paper, we define a -integral, i.e. an integral defined by means of partitions of unity, on a suitable compact metric measure space, whose measure is compatible with its topology in the sense that every open set is -measurable. We prove that the -integral is equivalent to -integral. Moreover, we give an example of a noneuclidean compact metric space such that the above results are true.
A Radon-Nikodym theorem for the v-integral.
A representation theorem for time-scale functionals
A summability integral.
A unified approach to Riesz type representation theorems
Algebraic genericity of strict-order integrability
We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and...
An example concerning automorphisms of generalized cubes
An inequality for correlated measurable functions.
An L...-Estimate for the gradient of extremals.
Application of Pettis integration to differential inclusions with three-point boundary conditions in Banach spaces.
Applications of decomposable measures on nonlinear difference equations.