A refinement of Ball's theorem on Young measures.
A remark on Slutsky's theorem
A Riemann approach to random variation
This essay outlines a generalized Riemann approach to the analysis of random variation and illustrates it by a construction of Brownian motion in a new and simple manner.
A Selection Lemma for Sequences of Measurable Sets, and Lower Semicontinuity of Multiple Integrals.
A simple characterization of almost uniform convergence by stochastic convergence.
A topological proof of Denjoy-Stepanoff theorem
A Тote on the Сompleteness of
Additive functions and singular measures
Additive functions modulo a countable subgroup of ℝ
We solve the mod G Cauchy functional equation f(x+y) = f(x) + f(y) (mod G), where G is a countable subgroup of ℝ and f:ℝ → ℝ is Borel measurable. We show that the only solutions are functions linear mod G.
Admissible functions in two-scale convergence.
Algebraic structures generated by almost continuous functions
Algebras of Borel measurable functions
We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Almost Everywhere First-Return Recovery
We present a new characterization of Lebesgue measurable functions; namely, a function f:[0,1]→ ℝ is measurable if and only if it is first-return recoverable almost everywhere. This result is established by demonstrating a connection between almost everywhere first-return recovery and a first-return process for yielding the integral of a measurable function.
Almost uniform convergence for continuous parameters
An addendum to a remark on Slutsky's theorem
An approximate analog of a theorem of Khintchine
An elementary proof of Komlós-Révész theorem in Hilbert spaces.
An extension of Brunovský's Scorza-Dragoni type theorem for unbounded set-valued functions
Analytic gaps
We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.
Approximate symmetric derivative and monotonicity