Related papers: A disintegration theorem
We study a version of the Lebesgue differentiation theorem in which the integral averages are replaced with medians over Busemann--Feller differentiation bases. Our main result gives several characterizations for the differentiation…
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new…
We develop a method that we call \emph{omission of intervals}, for establishing topological properties of subsets of the real line based on their combinatorial structure. Using this method, we obtain conceptual proofs of the fundamental…
The leading idea of the paper is to treat the theorem of Wigner with methods inspired by geometry. The exercise mentionned in the title has two functions: On the one hand it can serve as a pedagogical text in order to make the reader…
A sharp version of the Central Limit Theorem for linear combinations of iterates of an inner function is proved. The authors previously showed this result assuming a suboptimal condition on the coefficients of the linear combination. Here…
Starting with the Brezis-Browder principle, we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature. Relationships among the elements of different sets of assumptions are…
A common problem in various applications is the additive decomposition of the output of a function with respect to its input variables. Functions with binary arguments can be axiomatically decomposed by the famous Shapley value. For the…
This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent,…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…
Standard Bayesian inference can build models that combine information from various sources, but this inference may not be reliable if components of a model are misspecified. Cut inference, as a particular type of modularized Bayesian…
In a recent work [3], the authors established new results about general linear Mahler systems in several variables from the perspective of transcendental number theory, such as a multivariate extension of Nishioka's theorem. Working with…
Disentanglement via mechanism sparsity was introduced recently as a principled approach to extract latent factors without supervision when the causal graph relating them in time is sparse, and/or when actions are observed and affect them…
The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same multigrading, to produce a new homogeneous ideal. Toric fiber products generalize familiar constructions in commutative algebra like…
The notion of a separable extension is an important concept in Galois theory. Traditionally, this concept is introduced using the minimal polynomial and the formal derivative. In this work, we present an alternative approach to this…
We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability which is easier to guarantee computationally. We prove results…
Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then…
It is proposed a possible new approach of quantum measurements (QMS), disconnected of the traditional interpretation of uncertainty relations and independent of any appeal to the strange idea of collapse (reduction) of wave functions. The…
Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…
The question of what should be meant by a measurement is tackled from a mathematical perspective whose physical interpretation is that a measurement is a fundamental process via which a finite amount of classical information is produced.…