Random series of functions and Baire category
Wayne George Babinchuk · cIRcle (University of British Columbia) · 2010
In much of the work done on random series of functions, little attention has been given to the categorical questions that may arise. For example, a common technique is to let ε = {ε [sub n]}[sup ∞ sub n = 0] be a sequence of independent random variables, each taking the values ±1 with probability ½, and to consider the series [sup ∞]∑ [sub n = 0] ε[sub n]c[sub n] cos nt; then one can seek conditions on the coefficients {c[sub n]}[sup ∞ sub n = 0] that almost surely guarantee that the series converges or that it belongs to a certain function space. But one may also ask if this series converges for a set of e of second category or if it belongs to a particular space for such a set of ε. This thesis follows the first seven chapters of J.-P. Kahane's book Some Random Series of Functions and raises these kinds of categorical questions about the topics presented there.