A necessary and sufficient condition for the representation of a function as a Hankel-Stieltjes transform
A negative result in differentiation theory
A new approach to a hyperspace theory.
A new approach to function spaces on quasi-metric spaces.
A new class of Ornstein transformations with singular spectrum
A new model of the ergodic transformations
A new proof of Kelley's Theorem
Kelley's Theorem is a purely combinatorial characterization of measure algebras. We first apply linear programming to exhibit the duality between measures and this characterization for finite algebras. Then we give a new proof of the Theorem using methods from nonstandard analysis.
A new result of G. A. Edgar on representing points in a convex bounded subset of Banach spaces with the Radon-Nikodym property as barycentres of Radon measures
A new type of affine Borel function.
A noncommutative Orlicz-Pettis type theorem
A noncommutative version of a Theorem of Marczewski for submeasures
It is shown that every monocompact submeasure on an orthomodular poset is order continuous. From this generalization of the classical Marczewski Theorem, several results of commutative Measure Theory are derived and unified.
A noncompact Choquet theorem
A nonergodic version of Gordin's CLT for integrable stationary processes
A non-ergodic version of Rudolph's theorem
A nonlinear Banach-Steinhaus theorem and some meager sets in Banach spaces
We establish a Banach-Steinhaus type theorem for nonlinear functionals of several variables. As an application, we obtain extensions of the recent results of Balcerzak and Wachowicz on some meager subsets of L¹(μ) × L¹(μ) and c₀ × c₀. As another consequence, we get a Banach-Mazurkiewicz type theorem on some residual subset of C[0,1] involving Kharazishvili's notion of Φ-derivative.
A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension
We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.
A non-regular Toeplitz flow with preset pure point spectrum
Given an arbitrary countable subgroup of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to . For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.
A Nonstandard Approach to the Uniqueness Problem for the Navier-Stokes Equations.
A note on a generalized cohomology equation
We give a necessary and sufficient condition for the solvability of a generalized cohomology equation, for an ergodic endomorphism of a probability measure space, in the space of measurable complex functions. This generalizes a result obtained in [7].
A note on a local ergodic theorem