Partial results were obtained previously by K. F. Roth (1952) who established the existence of arithmetic progressions of length three in subsets of Z of positive upper density, and by E. Szemerédi… (More)

The factors influencing the range of motion of the knee after total condylar knee replacement were analyzed in fifty-five consecutive patients who had seventy-one replacements and a minimum follow-up… (More)

Given a measurable transformation on a measure space one can ask whether or not there is an equivalent measure that is invariant under the transformation. This problem is discussed very thoroughly in… (More)

For an area-preserving twist map F of a finite annulus, we obtain “quasi-foliations” of the annulus by one-sided-F -invariant graphs of functions that are either continuous (in which case the graph… (More)

Ergodic theory is the theory of the long-term statistical behavior of dynamical systems. The baker's transformation is an object of ergodic theory that provides a paradigm for the possibility of… (More)

Let P(x, ;y)=P(0, y — x) be the transition function of a random walk on the set of lattice points i ?= {x: x has integer valued coordinates} in d-dimensional Euclidean space, d^l. Thus 05^P(0, x),… (More)

The purpose of the present note is to sketch a solution for the problem of determining the form of all isometries of any reflexive Orlicz space. A partial result in that direction was obtained… (More)