4 papers
Nonstandard analysis of the behavior of ergodic means of dynamical systems on very big finite probability spaces
E. I. Gordon, L. Yu. Glebsky, C. W. Henson
The trivial proof of the ergodic theorem for a finite set and a permutation shows that for an arbitrary function the sequence of ergodic means $A…
Ergodic theorem for a Loeb space and hyperfinite approximations of dynamical systems
L. Yu. Glebsky, E. I. Gordon, C. W. Henson
Although the G.Birkhoff Ergodic Theorem (BET) is trivial for finite spaces, this does not help in proving it for hyperfinite Loeb spaces. The proof of the BET for this case, sugges…
A theory of hyperfinite sets
P. V. Andreev, E. I. Gordon
We develop an axiomatic set theory -- the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theore…
On finite approximations of topological algebraic systems
L. Yu. Glebsky, E. I. Gordon, C. W. Henson
We introduce and discuss a definition of approximation of a topological algebraic system by finite algebraic systems of some class $\K$. For the case of a discrete algebraic sy…