Random series of functions and Baire category
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 probabilit...
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| Language: | English |
| Published: |
2010
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| Online Access: | http://hdl.handle.net/2429/19479 |
| Summary: | 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. === Science, Faculty of === Mathematics, Department of === Graduate |
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