Let X be an arbitrary nonempty set and a lattice of subsets of X such that φ, X∈ . ( ) is the algebra generated by and ( ) denotes those nonnegative, finite, finitely additive measures μ on ( ). I( ) denotes the subset of ( ) of nontrivial zeroone valued measures. Associated with μ ∈ I( ) (or Iσ ( )) are the outer measures μ′ and μ′′ considered in detail. In addition, measurability conditions a...

It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality--independent of the state and the measurements chosen at the other site. In this Letter we prove the converse: every pair of incompatible quantum observables enables the violation of a Bell inequality and therefore must remain incompatible within any other no-signaling theory. While in the cas...

The lack of measurability of the empirical process with respect to the sigma-field generated by the ‘natural’ l∞ metric, as illustrated in the previous notes, needs an extension of the standard weak convergence theory that can handle situations where the converging stochastic processes may no longer be measurable (though the limit will be a tight Borel measurable random element). Of course, an ...

Abstract It is well known that in gauge theories, the spin (and orbital angular momentum) of gauge particles is not gauge invariant, although the helicity is; neither are the canonical momentum and canonical angular momentum of charged particles. However, the simple appeal of these concepts has motivated repeated attempts to resurrect them as physical descriptions of gauge systems. In particula...

We present a model where ω1 is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more recently continued by Schrittesser and Friedman (see [7]), regarding the separation of different notions of regularity properties of the real line. Acknowledgement. T...

A bounded function φ : G → C on an LCA group G is called Hartman measurable if it can be extended to a Riemann integrable function φ∗ : X → C on some group compactification (ιX , X), i.e. on a compact group X such that ιX : G → X is a continuous homomorphism with image ιX(G) dense in X and φ = φ ∗ ◦ ιX . The concept of Hartman measurability of functions is a generalization of Hartman measurabil...

We prove that for all standard arboreal forcing notions P there is a counterexample for the implication “If A is determined, then A is P-measurable”. Moreover, we investigate for which forcing notions this is extendible to “weakly P-measurable”.