A set of infinite measure whose ratio set does not contain a given sequence.
A Short Proof of a Theorem of Ruelle.
A short proof of the Hausdorff dimension formula for Lévy processes.
A short zero-one law proof of a result of Abian.
A simple characterization of almost uniform convergence by stochastic convergence.
A Simple Example of Pathological Submeasure.
A simple proof that determinacy implies Lebesgue measurability.
A simplified multidimensional integral
We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.
A solution to the problem of B. V. Rao on Borel structures
A stabilization property and its applications in the theory of sections
A stabilization property and its applications in theory of sections
A summability integral.
A survey on lifting in measure theory
A Theorem on the Extension of Measures in Uniform Spaces
A topological proof of Denjoy-Stepanoff theorem
A unified approach to Riesz type representation theorems
A uniform dimension result for two-dimensional fractional multiplicative processes
Given a two-dimensional fractional multiplicative process determined by two Hurst exponents and , we show that there is an associated uniform Hausdorff dimension result for the images of subsets of by if and only if .
A uniqueness property for measures on
A uniqueness result for the continuity equation in two dimensions
We characterize the autonomous, divergence-free vector fields on the plane such that the Cauchy problem for the continuity equation admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential associated to . As a corollary we obtain uniqueness under the assumption that the curl of is a measure. This result can be extended to certain non-autonomous vector fields with bounded divergence....
A universal null graph whose domain has positive measure