Related papers: Borel version of the Local Lemma
Tests of Bell's theorem rule out local hidden variables theories. But any theorem is only as good as the assumptions that go into it, and one of these assumptions is that the experimenter can freely chose the detector settings. Without this…
Reviewing the general representation of a stochastic local hidden variables theory in the context of an ideal Bohm's version of the EPR experiment, we show explicitly that the violation of Bell's locality condition is due to the assumption…
The characterisation of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic…
We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…
Pearl and Verma developed d-separation as a widely used graphical criterion to reason about the conditional independencies that are implied by the causal structure of a Bayesian network. As acyclic ground probabilistic logic programs…
Testing a hypothesized causal model against observational data is a key prerequisite for many causal inference tasks. A natural approach is to test whether the conditional independence relations (CIs) assumed in the model hold in the data.…
We show that every countable Borel equivalence relation structurable by $n$-dimensional contractible simplicial complexes embeds into one which is structurable by such complexes with the further property that each vertex belongs to at most…
Using representation theory techniques we prove that various spaces of derivations or one-sided multipliers over certain operator algebras are reflexive. A sample result: any bounded local derivation (local left multiplier) on an…
In the framework of the probabilistic method in combinatorics, we revisit the entropy compression method clarifying the setting in which it can be applied and providing a theorem yielding a general constructive criterion. We finally…
We present a constructive proof of Brouwer's fixed point theorem for uniformly continuous and sequentially locally non-constant functions based on the existence of approximate fixed points. And we will show that Brouwer's fixed point…
A local Tb Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator T. One needs only boundedness of the operator T on systems of locally pseudo-accretive functions \{b_Q\}, indexed by cubes. We…
Nadkarni's Theorem asserts that for a countable Borel equivalence relation (CBER) exactly one of the following holds: (1) It has an invariant Borel probability measure or (2) it admits a Borel compression, i.e., a Borel injection that maps…
We study here the topology of information on the space of probability measures over Polish spaces that was defined in [1]. We show that under this topology, a convergent sequence of probability measures satisfying a conditional independence…
Recent work of the author established dual representation theorems for certain vector spaces that arise in an important article of Allcock and Vaaler. These results constructed an object called a consistent map which acts like a measure on…
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the…
We reinterpret a conjecture of Breuil on the locally analytic $\mathrm{Ext}^1$ in a functorial way using $(\varphi,\Gamma)$-modules (possibly with $t$-torsion) over the Robba ring, making it more accurate. Then we prove several special or…
It is known that for $X$ a nowhere locally compact metric space, the set of bounded continuous, nowhere locally uniformly continuous real-valued functions on $X$ contains a dense $G_\delta$ set in the space $C_b(X)$ of all bounded…
Our main aim in this self-contained article is at the same time to detail the relationships between the resurgence and the hyperasymptotic theories, and to demonstrate how these theories can be used for an implicit resurgent function. For…
Learning a Bayesian network structure from data is an NP-hard problem and thus exact algorithms are feasible only for small data sets. Therefore, network structures for larger networks are usually learned with various heuristics. Another…
In the present note, we generalize the first part of the Borel-Cantelli lemma. By this generalization, we obtain some strong limit results.