Mutual dimension, data processing inequalities, and randomness

This dissertation makes progress in the area of constructive dimension, an effectivization of classical Hausdorff dimension. Using constructive dimension, one may assign a non-zero number to the dimension of individual sequences and individual points in Euclidean space. The primary objective of this dissertation is to develop a framework for mutual dimension, i.e., the density of algorithmic mutual information between two infinite objects, that has similar properties as those of classical Shannon mutual information. (Abstract shortened by ProQuest.).