Related papers: On Buck's measurability of certain sets
In this paper, concept of possibility neutrosophic soft set and its operations are defined, and their properties are studied. An application of this theory in decision making is investigated. Also a similarity measure of two possibility…
Kernel density estimation is a popular method for estimating unseen probability distributions. However, the convergence of these classical estimators to the true density slows down in high dimensions. Moreover, they do not define meaningful…
Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…
The notion of density of a finite set is discussed. We proof a general theorem of set theory which refines Bose-Einstein distribution.
This paper considers the relevance of the concepts of observability and computability in physical theory. Observability is related to verifiability which is essential for effective computing and as physical systems are computational systems…
Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group invariant introduced by Leptin in 1966. We then restrict to unimodular amenable groups and to…
Let $K\subset R^n$ be a compact basic semi-algebraic set. We provide a necessary and sufficient condition (with no a priori bounding parameter) for a real sequence $y=(y_\alpha)$, $\alpha\in N^n$, to have a finite representing Borel measure…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model.…
This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
We consider the problems of hypothesis testing on a probability measure of independent sample, on solution of ill-posed problem, on deconvolution problem and on Poisson mean measure. For all these setups necessary conditions and sufficient…
I explore the use of sets of probability measures as a representation of uncertainty.
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
Let $\mathrm{d}(A)$ be the asymptotic density (if it exists) of a sequence of integers $A$. For any real numbers $0\leq\alpha\leq\beta\leq 1$, we solve the question of the existence of a sequence $A$ of positive integers such that…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
The question of quantifying the sharpness (or unsharpness) of a quantum mechanical effect is investigated. Apart from sharpness, another property, bias, is found to be relevant for the joint measurability or coexistence of two effects.…
We investigate some properties of density measures -- finitely additive measures on the set of natural numbers $\N$ extending asymptotic density. We introduce a class of density measures, which is defined using cluster points of the…
The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…
A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…