Related papers: On submeasures on Boolean algebras
We prove the consistency with ZFC of ``the length of an ultraproduct of Boolean algebras is smaller than the ultraproduct of the lengths''. Similarly for some other cardinal invariants of Boolean algebras.
We define holonomic measures to be certain analogues of varifolds that keep track of the local parameterization and orientation of the submanifold they represent. They are Borel measures on the direct sum of several copies of the tangent…
The paper concerns the theory of parabolic equations on a broad class of closed subsets of Euclidean space possessing a kind of tangent structure. A necessary framework for considering evolutionary problems is developed, and fundamental…
In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a…
Our aim is to explain instances in which the value of the logarithmic Mahler measure of a polynomial can be written in an unexpectedly neat manner. To this end we examine polynomials defining rational curves, which allows their zero-locus…
We study many properties concerning weak K\"ahlerianity on compact complex manifolds which admits a holomorphic submersion onto a K\"ahler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the K\"ahler…
We show that the open problem presented in "Geometric Folding Algorithms: Linkages, Origami, Polyhedra" [DO07] is solved by a theorem of Burago and Zalgaller [BZ96] from more than a decade earlier.
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
We show that the variety of symmetric implication algebras is generated from cubic implication algebras and Boolean algebras. We do this by developing the notion of a locally symmetric implication algebra that has properties similar to…
John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued…
In this short note, we construct a variant of the Bohr topos of a C*-algebra which takes into account the topology of the algebra in a finer way and such that this construction is stable under pullback along geometric morphisms. This…
We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.
A solution to the effectiveness problem in Kohn's algorithm for generating subelliptic multipliers is provided for domains that include those given by sums of squares of holomorphic functions (also including infinite sums). These domains…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
This article presents a proof of the Feldman-Moore theorem on Cartan subalgebras in W*-algebras based on the non-commutative Stone equivalence between Boolean inverse semigroups and Boolean groupoids. The proof is decomposed into two parts.…
We show how the measure theory of regular compacted-Borel measures defined on the $\delta$-ring of compacted-Borel subsets of a weighted locally compact group $(G,\omega)$ provides a compatible framework for defining the corresponding…
We introduce and study bimeasurings from pairs of bialgebras to algebras. It is shown that the universal bimeasuring bialgebra construction, which arises from Sweedler's universal measuring coalgebra construction and generalizes the finite…
We solve a Lehmer-type question about the Mahler measure of integer-valued polynomials.
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…