We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomor-phic to the measure algebra of 2 ! 1. The rst construction uses } to produce an S-space with no convergent sequences in which every perfect set is a G. A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The sec...

It is shown that every Radon measure on a first-countable Hausdorff space is separable provided ω1 is a precaliber of every measurable algebra. As the latter is implied by MA(ω1), the result answers a problem due to D. H. Fremlin. Answering the problem posed by D. H. Fremlin ([4], 32R(c)), we show in this note that, assuming (∗) ω1 is a precaliber of every measurable Boolean algebra, every Rado...

Interval-valued fuzzy sets are based on the algebra of subintervals of the unit interval [0, 1]. We study valuations as a special type of measures on this algebra. We present a description of all valuations which preserve the standard fuzzy negation and extend the identity on the elements of the form (x, x). Consequences for sublattices are formulated. Keywords— Girard algebra, interval-valued ...

We study the measure theory of a two-site quantum random walk. The truncated decoherence functional defines a quantum measure μn on the space of n-paths, and the μn in turn induce a quantum measure μ on the cylinder sets within the space Ω of untruncated paths. Although μ cannot be extended to a continuous quantum measure on the full σ-algebra generated by the cylinder sets, an important questi...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

We prove, by a straight construction, that the automorphism group of the measure algebra and the subgroup of the measure preserving ones cannot be isomorphic to the trivial automorphisms of P(N)/fin.

Recently, Sahlmann [1] proposed a new, algebraic point of view on the loop quantization. He brought up the issue of a ⋆-algebra underlying that framework, studied the algebra consisting of the fluxes and holonomies and characterized its representations. We define the diffeomorphism covariance of a representation of the Sahlmann algebra and study the diffeomorphism covariant representations. We ...

for any finite disjoint union ∪j=1Aj ×Bj of rectangles. It is easy to see, by considering a common refinement of any two representations of a set in A as a finite disjoint union of rectangles that m does not depend on the representation, and is well-defined premeasure on A. 1.2 DEFINITION (Product sigma-algebra). For any two measure spaces (X,M, μ) and (Y,N , μ), the product sigma algebra in X ...

Recently, Sahlmann [1] proposed a new, algebraic point of view on the loop quantization. He brought up the issue of a ⋆-algebra underlying that framework, studied the algebra consisting of the fluxes and holonomies and characterized its representations. We define the diffeomorphism covariance of a representation of the Sahlmann algebra and study the diffeomorphism covariant representations. We ...