Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On processes which cannot be distinguished by finitary observation   A function $J$ defined on a family $C$ of stationary processes is finitely
observable if there is a sequence of functions $s_n$ such that $s_n(x_1 ...
x_n)\to J(X)$ in probability for every process $X=(x_n)\in C$. Recently,
Ornstein and Weiss roved the striking result that if $C$ is the class of
aperiodic ergodic finite valued processes, then the only finitely observable
isomorphism invariant on $C$ is entropy. We sharpen this in several ways. Our
main theorem is that if $X \to Y$ is a zero-entropy extension of finite entropy
ergodic systems and $C$ is the family of processes arising from $X$ and $Y$,
then every finitely observable function on $C$ is constant. This implies
Ornstein and Weiss' result, and extends it to many other families of processes,
e.g. it shows that there are no nontrivial finitely observable isomorphism
invariants for processes arising from Kronecker systems, mild and strong mixing
zero entropy systems. It also implies that any finitely observable isomorphism
invariant defined on the family of processes arising from irrational rotations
must be constant for rotations belonging to a set of full Lebesgue measure.

24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol