An analog of Sard's theorem for -smooth functions of two variables.
An analog of the Marcinkiewicz integral in ergodic theory
An analogue of a result of Carathéodory
An analogue of the Variational Principle for group and pseudogroup actions
We generalize to the case of finitely generated groups of homeomorphisms the notion of a local measure entropy introduced by Brin and Katok [7] for a single map. We apply the theory of dimensional type characteristics of a dynamical system elaborated by Pesin [25] to obtain a relationship between the topological entropy of a pseudogroup and a group of homeomorphisms of a metric space, defined by Ghys, Langevin and Walczak in [12], and its local measure entropies. We prove an analogue of the Variational...
An analytic study on the self-similar fractals: Differentiation of integrals.
An answer to a question by J. Milnor.
An anti-classification theorem for ergodic measure preserving transformations
Despite many notable advances the general problem of classifying ergodic measure preserving transformations (MPT) has remained wide open. We show that the action of the whole group of MPT’s on ergodic actions by conjugation is turbulent in the sense of G. Hjorth. The type of classifications ruled out by this property include countable algebraic objects such as those that occur in the Halmos–von Neumann theorem classifying ergodic MPT’s with pure point spectrum. We treat both the classical case of...
An Application of Shoenfield's Absoluteness Theorem to the Theory of Uniform Distribution.
An approximate analog of a theorem of Khintchine
An area formula in metric spaces
We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure-theoretic notion of Jacobian, defined as the density of a suitable "pull-back measure". Finally, we give some applications and examples.
An atomic theory of ergodic spaces
An axiomatic approach to Quantum Gauge Field Theory
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge transformations. That is, we propose a new set of Osterwalder Schrader like axioms for the characteristic functional of a measure on the space of generalized connections modulo gauge transformations rather than for the associated Schwinger distributions. We show non-triviality...
An axiomatic definition of the entropy of a -action on a Lebesgue space
An Egoroff-type theorem for set-valued measurable functions.
An Elementary Characterization of Absolutely Summing Operators.
An Elementary Lemma on Sequences of Integers and Its Apllications to Functional Analysis.
An elementary proof of Hawkes's conjecture on Galton-Watson trees.
An elementary proof of Komlós-Révész theorem in Hilbert spaces.
An elementary proof of the Fubini-Stone theorem
An Equipartition of Planar Sets.