Split Faces and Projective Sets in a Metrizable Compact Convex Set.
Stability of Lewis and Vogel's result.
Stable intersections of Cantor sets and homoclinic bifurcations
Statistical convergence of a sequence of random variables and limit theorems
In this paper the ideas of three types of statistical convergence of a sequence of random variables, namely, statistical convergence in probability, statistical convergence in mean of order and statistical convergence in distribution are introduced and the interrelation among them is investigated. Also their certain basic properties are studied.
Stetigkeitsaussagen zur Diskussion des Schnittverhaltens einer Ovalenschar mit einem Oval
Stretched shadings and a Banach measure that is not scale-invariant
It is shown that if A ⊂ ℝ has the same constant shade with respect to all Banach measures, then the same is true of any similarity transformation of A and the shade is not changed by the transformation. On the other hand, if A ⊂ ℝ has constant μ-shade with respect to some fixed Banach measure μ, then the same need not be true of a similarity transformation of A with respect to μ. But even if it is, the μ-shade might be changed by the transformation. To prove such a μ exists, a Hamel basis with some...
Strict topology and perfect measures
Strong bifurcation loci of full Hausdorff dimension
In the moduli space of degree rational maps, the bifurcation locus is the support of a closed positive current which is called the bifurcation current. This current gives rise to a measure whose support is the seat of strong bifurcations. Our main result says that has maximal Hausdorff dimension . As a consequence, the set of degree rational maps having distinct neutral cycles is dense in a set of full Hausdorff dimension.
Strong continuity of invariant probability charges
Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0,1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.
Strong differentiability with respect to product measures
Strong essential cluster sets.
Strong Fubini axioms from measure extension axioms
It is shown that measure extension axioms imply various forms of the Fubini theorem for nonmeasurable sets and functions in Radon measure spaces.
Strong Fubini properties for measure and category
Let (FP) abbreviate the statement that holds for every bounded function f: [0,1]² → ℝ whenever each of the integrals involved exists. We shall denote by (SFP) the statement that the equality above holds for every bounded function f: [0,1]² → ℝ having measurable vertical and horizontal sections. It follows from well-known results that both of (FP) and (SFP) are independent of the axioms of ZFC. We investigate the logical connections of these statements with several other strong Fubini type properties...
Strong Fubini properties of ideals
Let I and J be σ-ideals on Polish spaces X and Y, respectively. We say that the pair ⟨I,J⟩ has the Strong Fubini Property (SFP) if for every set D ⊆ X× Y with measurable sections, if all its sections are in J, then the sections are in I for every y outside a set from J (“measurable" means being a member of the σ-algebra of Borel sets modulo sets from the respective σ-ideal). We study the question of which pairs of σ-ideals have the Strong Fubini Property. Since CH excludes this phenomenon completely,...
Strong measure zero and meager-additive sets through the prism of fractal measures
We develop a theory of sharp measure zero sets that parallels Borel’s strong measure zero, and prove a theorem analogous to Galvin–Mycielski–Solovay theorem, namely that a set of reals has sharp measure zero if and only if it is meager-additive. Some consequences: A subset of is meager-additive if and only if it is -additive; if is continuous and is meager-additive, then so is .
Strongly nonlinear potential theory on metric spaces.
Structure fractals and para-quaternionic geometry
It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...
Studies of some items of the lattice theory in relation to the Hilbert-Hermite space
Subadditive measures and small systems
Submeasure and measure