Related papers: Models of Cohen measurability
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
In this article we will investigate nonmeasurability with respect to some $\sigma$-ideals in Polish space $X,$ of images of subsets of $X$ by selected mappings defined on the space $X$. Among of them we answer the following question: "It is…
A classical theorem of Menshov states that every measurable function can redefined on a set of arbitrarily small Lebesgue measure, so that the resulting function has uniformly convergent Fourier series. We prove that the same is true if we…
In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in…
A function f:R -> R is approximately continuous iff it is continuous in the density topology, i.e., for any ordinary open set U the set E=f^{-1}(U) is measurable and has Lebesgue density one at each of its points. Denjoy proved that…
We study the consistency strength of Lebesgue measurability for $\Sigma^1_3$ sets over Zermelo set theory ($Z$) in a completely choiceless context. We establish a result analogous to the Solovay-Shelah theorem.
The Axiom of Full Reflection at a measurable cardinal has been conjectured to be equiconsitent with the existence of a coherent sequence of measures with a repeat point. However we prove that the Axiom of Full Reflection at a measurable…
We prove several consistency results concerning the notion of $\omega$-strongly measurable cardinal in HOD. In particular, we show that is it consistent, relative to a large cardinal hypothesis weaker than $o(\kappa) = \kappa$, that every…
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…
We prove (ZF+DC) e.g. : if mu =|H(mu)| then mu^+ is regular non measurable. This is in contrast with the results for mu = aleph_{omega} on measurability see Apter Magidor [ApMg]
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no-go arguments against non-contextual hidden variables. All such arguments rely on choosing special sets of quantum-mechanical…
We formulate the conditions under which the dynamics of a continuously measured quantum system becomes indistinguishable from that of the corresponding classical system. In particular, we demonstrate that even in a classically chaotic…
Classical theorem of Luzin states that a measurable function of one real variable is "almost" continuous. For measurable functions of several variables the analogous statement (continuity on the product of sets having almost full measure)…
The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space,…
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the…
A pointwise definable model is one in which every object is definable without parameters. In a model of set theory, this property strengthens V=HOD, but is not first-order expressible. Nevertheless, if ZFC is consistent, then there are…
It is studied a connection between the separability and the countable chain condition of spaces with the $L$-property (a topological space $X$ has the $L$-property if for every topological space $Y$, separately continuous function…
We show in ZFC that there is no set of reals of size continuum which can be translated away from every set in the Marczewski ideal. We also show that in the Cohen model, every set with this property is countable.
Let the measure algebra of a topological group be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly…
In this article we introduce the new modulus $\triangle'_{X,\phi}(\varepsilon)$, for which we prove that in the general case is different from the classical modulus of noncompact convexity. The main result of the paper is showing the…