À propos d'un lemme de Tadeusz Ważewski
A pseudo Laguerre method
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 -linear automorphism of the reals with non-measurable graph
This note contains a proof of the existence of a one-to-one function of onto itself with the following properties: is a rational-linear automorphism of , and the graph of is a non-measurable subset of the plane.
A Radon-Nikodym derivative for positive linear functionals
An exact Radon-Nikodym derivative is obtained for a pair (I,J) of positive linear functionals, with J absolutely continuous with respect to I, using a notion of exhaustion of I on elements of a function algebra lattice.
A Radon-Nikodym theorem for the v-integral.
A reconsideration of Hua's inequality.
A reconsideration of Hua's inequality. II.
A refinement of an inequality from information theory.
A refinement of Hölder's inequality and applications.
A refinement of Jensen's inequality.
A refinement of Jensen's inequality for a class of increasing and concave functions.
A refinement of the Poincaré inequality for Kolmogorov operators on .
A refinement of van der Corput's inequality.
A refinement of various mean inequalities.
A relation to Hardy-Hilbert's integral inequality and Mulholland's inequality.
A relation to Hilbert's integral inequality and some base Hilbert-type inequalities.
A relationship between intersection conditions and porosity conditions for local systems
A relaxation result in BV for integral functionals with discontinuous integrands
We prove a relaxation theorem in BV for a non coercive functional with linear growth. No continuity of the integrand with respect to the spatial variable is assumed.
A remark on functions continuous on all lines
We prove that each linearly continuous function on (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for on an arbitrary Banach space , if has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such on a separable is continuous at all points outside a first category set which is also null in any usual sense.