| Thesis Details |
 Title | Average co-ordinate entropy and a
non-singular version of restricted
orbit equivalence |
|
Author | Mortiss, Genevieve Catherine |
|
Institution | University of New South Wales |
|
Date | 1997 |
|
Abstract | A notion of entropy is defined for the
non-singular action of finite co-ordinate
changes on X - the infinite product of two-
point spaces. This quantity - average
co-ordinate or AC entropy - is calculated
for product measures and G-measures on X,
and an equivalence relation is established
for which AC entropy is an invariant. The
Inverse Vitali Lemma is discussed in a
measure preserving context, and it is shown
that for a certain class of measures on
X known as odometer bounded, the result
will still hold for odometer actions.
The foundations for a non-singular version
of Rudolph's restricted orbit equivalence
are established, and a size for non-singular
orbit equivalence is introduced. It is shown
that provided the Inverse Vitali Lemma
still holds, the non-singular orbit equivalence
classes can be described using this new size. |
| Thesis
|
01front.pdf 204.4 Kb
02main.pdf 605.7 Kb
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