Families of pairwise orthogonal measures
Filippov Lemma for certain second order differential inclusions
In the paper we give an analogue of the Filippov Lemma for the second order differential inclusions with the initial conditions y(0) = 0, y′(0) = 0, where the matrix A ∈ ℝd×d and multifunction is Lipschitz continuous in y with a t-independent constant l. The main result is the following: Assume that F is measurable in t and integrably bounded. Let y 0 ∈ W 2,1 be an arbitrary function fulfilling the above initial conditions and such that where p 0 ∈ L 1[0, 1]. Then there exists a solution y ∈ W 2,1...
Finite Product of Semiring of Sets
We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].
Formes linéaires positives et mesures
Frame monomorphisms and a feature of the -group of Baire functions on a topological space
“The kernel functor” from the category of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In , monics are one-to-one, but not necessarily so in LFrm. An embedding for which is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The -objects every embedding of which is KI are characterized;...
Gaussian measures and covering theorems
Gemeinsame Urbilder endlich additiver Inhalte.
Generalizations of analytic and standard measurable spaces.
Generalized Lusin sets with the Blackwell property
Generalized Vitali systems of uniform type
Generation of operation-invariant classes of sets
Generic power series on subsets of the unit disk
We examine the boundary behaviour of the generic power series with coefficients chosen from a fixed bounded set in the sense of Baire category. Notably, we prove that for any open subset of the unit disk with a nonreal boundary point on the unit circle, is a dense set of . As it is demonstrated, this conclusion does not necessarily hold for arbitrary open sets accumulating to the unit circle. To complement these results, a characterization of coefficient sets having this property is given....
Hadamard-type inequalities for quasiconvex functions.
Hausdorff measures and two point set extensions
We investigate the following question: under which conditions is a σ-compact partial two point set contained in a two point set? We show that no reasonable measure or capacity (when applied to the set itself) can provide a sufficient condition for a compact partial two point set to be extendable to a two point set. On the other hand, we prove that under Martin's Axiom any σ-compact partial two point set such that its square has Hausdorff 1-measure zero is extendable.
Hellinger-Hahn type decompositions of the domain of Borel function
Hereditary measurable sets and universal measure
Hyper-extensions of -algebras
Infinite combinatorics in Function spaces: Category methods
Inscribing closed non--lower porous sets into Suslin non--lower porous sets.
Inscribing compact non-σ-porous sets into analytic non-σ-porous sets
The main aim of this paper is to give a simpler proof of the following assertion. Let A be an analytic non-σ-porous subset of a locally compact metric space, E. Then there exists a compact non-σ-porous subset of A. Moreover, we prove the above assertion also for σ-P-porous sets, where P is a porosity-like relation on E satisfying some additional conditions. Our result covers σ-⟨g⟩-porous sets, σ-porous sets, and σ-symmetrically porous sets.