Measurable weak sections

Critical Sections and Producer/Consumer Queues in Weak Memory Systems

In machines with weak memory consistency models , the ordering constraints on memory accesses are few. In order to properly program these machines, certain powerful explicit synchronization instructions are additionally provided by their architecture. We show that although a solution to the critical section problem (also referred to as the mutual exclusion problem) is impossible without such po...

Measurable Utility and the Measurable Choice Theorem

A note on copies of c 0 in spaces of weak * measurable functions

If (Ω,Σ, μ) is a finite measure space and X a Banach space, in this note we show that L w (μ,X∗), the Banach space of all classes of weak* equivalent X∗-valued weak* measurable functions f defined on Ω such that ‖f(ω)‖ ≤ g(ω) a.e. for some g ∈ L1(μ) equipped with its usual norm, contains a copy of c0 if and only if X∗ contains a copy of c0.

Measurable Transformations

Measurable Sensitivity

We introduce the notions of measurable and strong measurable sensitivity, which are measure-theoretic versions of the conditions of sensitive dependence on initial conditions and strong sensitive dependence on initial conditions, respectively. Strong measurable sensitivity is a consequence of light mixing, implies that a transformation has only finitely many eigenvalues, and does not exist in t...