A Construction of Uncountably Many Weak von Neumann Transformations

On Ulam-von Neumann Transformations

We define and study Ulam-von Neumann transformations which are certain interval mappings and conjugate to q(x) = 1 — 2x on [—1,1]. We use a singular metric on [—1,1] to study a Ulam-von Neumann transformation. This singular metric is universal in the sense that it does not depend on any particular mapping but only on the exponent of this mapping at its unique critical point. We give the smooth ...

Spaces of Uncountably Many Dimensions*

Riemann in his Habilitations Schrift of 1854 suggested the notion of ^-dimensional space (where n is a natural number) as an extension of the notion of three-dimensional euclidean space. Hubert extended the notion still further by defining a space of a countably infinite number of dimensions. Fréchetf in 1908 defined two other spaces of countably many dimensions, which he called D„ and J3W. Tyc...

A von Neumann Morgenstern Representation Result without Weak Continuity Assumption

In the paradigm of von Neumann and Morgenstern, a representation of a ne preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on a real open...

UNCOUNTABLY MANY DIFFERENT INVOLUTIONS OF 5s

Weak values are universal in von Neumann measurements.

We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system observable. For any coupling strength, any initial states, and any choice of conditioning, the averages of the detector position and momentum are completely des...