Nonadditive measure-theoretic pressure and applications to dimensions of an ergodic measure

Measure-theoretic Applications of Higher Demuth Randomness

We investigate measure-theoretic aspects of various notions of reducibility by applying analogs of Demuth’s Theorem in the hyperarithmetic and set-theoretic settings.

An Optical Measurement System to Measure Velocity and Provide Shock Wave Pressure Diagrams

This paper introduces an optical measurement system for shock wave characteristics. The system works by mountinga metal plate attached to spring mounts against the shock wavefront. This set is sealed and can plot the shock wave pressure diagram by measuring plate's displacement, radiation and changing the reflection of light during shock wave conflict, and converting these optical data to volta...

Asymptotic Distribution of Divergence Measure with Applications

Measure Theoretic Characterization of Multiresolution Frames in Higher Dimensions

We extend some of the classical results of the theory of multiresolution analysis (MRA) frames to Euclidean space Rd; d > 1; and provide relevant examples. In the process, we use the theory of shift-invariant subspaces to bring new insights to the theory of frame multiresolution analysis. In particular, we establish an analogue of the Mallat-Meyer algorithm for multidimensional MRA frames when ...

Measure Theoretic Probability

Preface In these notes we explain the measure theoretic foundations of modern probability. The notes are used during a course that had as one of its principal aims a swift introduction to measure theory as far as it is needed in modern probability, e.g. to define concepts as conditional expectation and to prove limit theorems for martingales. Everyone with a basic notion of mathematics and prob...