相关论文: Algebraic characterizations of measure algebras
In this paper, we have obtained a necessary and suffcient condition for the series.
Uniform measures are defined as the functionals on the space of bounded uniformly continuous functions that are continuous on bounded uniformly equicontinuous sets. If every cardinal has measure zero then every countably additive measure is…
We prove that for any superatomic Boolean Algebra of cardinality >beth_omega there is an automorphism moving uncountably many atoms. Similarly for larger cardinals. Any of those results are essentially best possible.
The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
We prove that assuming suitable cardinal arithmetic, if B is a Boolean algebra every homomorphic image of which is isomorphic to a factor, then B has locally small density. We also prove that for an (infinite) Boolean algebra B, the number…
Let $X$ be a Banach space and $(\Omega,\Sigma)$ be a measure space. We provide a characterization of sequences in the space of $X$-valued countably additive measures on $\Omega,\Sigma)$ of bounded variation that generate complemented copies…
The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…
We study when a map between two subsets of a Boolean domain W can be extended to an automorphism of W. Under many hypotheses, if the underlying Boolean algebra is complete or if the sets are finite or Boolean domains, the necessary and…
The note complements topological aspects of the theory of chiral algebras.
In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh…
We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusion-exclusion principle.
We define a general notion of "summability" of a set $I\subseteq\mathbb{C^{N}}$ and show that some trivial condition necessary for a set to be summable, is also sufficient. We deduce some intresting corollaries.
We obtain a set of necessary and sufficient conditions for $| \bar{N}, p_{n} |_{k} $ to imply $|\bar{N}, q_{n} |_{s}$ for $1 < k \leq s < \infty$. Using this result we establish several inclusion theorems as well as conditions for the…
We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…
In this paper, we present a new axiomatic system that is a minimal axiomatization of Boolean algebras. Furthermore, the symmetric difference is shown to be algebraically analogous to the modular difference of two numbers. Finally, a new…
We present a collection of observations and results concerning submeasures on Boolean algebras. They are all motivated by Maharam's problem and Talagrand's construction that solved it.
We find necessary and sufficient conditions on a family $\mathcal{R} = (r_i)_{i \in I}$ in a Boolean algebra $\mathcal{B}$ under which there exists a unique positive probability measure $\mu$ on $\mathcal{B}$ such that $\mu (…
For a hyperbolic polynomial automorphism of $\C^2$, we show the existence of a measure of maximal dimension, and identify the conditions under which a measure of full dimension exists.