相关论文: How behave the typical $L^q$-dimensions of measure…

We study the decay of $\mu(B(x,r)\cap C)/\mu(B(x,r))$ as $r\downarrow 0$ for different kinds of measures $\mu$ on $\R^n$ and various cones $C$ around $x$. As an application, we provide sufficient conditions implying that the local…

We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…

In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…

We consider unitary polynomials $P \in Z[X]$ whose roots $(x_i)$ belong to a given compact $K$ of $C$. To such a polynomial we associate the measure $\mu_P$ on $K$ which is the mean value of the Dirac measures $\delta_{x_i}$. What are the…

We construct the entropic measure $\mathbb{P}^\beta$ on compact manifolds of any dimension. It is defined as the push forward of the Dirichlet process (another random probability measure, well-known to exist on spaces of any dimension)…

We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…

We study various measure theories using the classical approach and then compute the Hausdorff dimension of some simple objects and self-similar fractals. We then develop a nonstandard approach to these measure theories and examine the…

The probability density quantile (pdQ) carries essential information regarding shape and tail behavior of a location-scale family. Convergence of repeated applications of the pdQ mapping to the uniform distribution is investigated and new…

Let $(\mathcal{X},\rho)$ be a metric space and $\lambda$ be a Borel measure on this space defined on the $\sigma$-algebra generated by open subsets of $\mathcal{X}$; this measure $\lambda$ defines volumes of Borel subsets of $\mathcal{X}$.…

Let $\mu$ be the self-similar measure supported on the self-similar set $K$ with open set condition. In this article, we discuss the packing dimension of the set $\{x\in K: A(\frac{\log\mu(B(x,r))}{\log r})=I\}$ for $I\subseteq\mathbb{R}$,…

For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…

For infinite measure-theoretic entropy systems, we introduce the notion of measure-theoretic metric mean dimension of invariant measures for different types of measure-theoretic $\epsilon$-entropies, and show that measure-theoretic metric…

After a recollection on compression through a projection onto a polyhedral set (which generalizes the compression by coordinates quantization), we express, in this framework, the probability that an image is coded with $K$ coefficients as…

We study the L^q -dimensions of self-affine measures and the Kaenmaki measure on a class of self-affine sets similar to the class considered by Hueter and Lalley. We give simple, checkable conditions under which the Lq -dimensions are equal…

We study variational principles for metric mean dimension. First we prove that in the variational principle of Lindenstrauss and Tsukamoto it suffices to take supremum over ergodic measures. Second we derive a variational principle for…

For a compact subset K of the plane and a point x, we define the visible part of K from x to be the set K_x={u\in K : [x,u]\cap K={u}}. (Here [x,u] denotes the closed line segment joining x to u.) In this paper, we use energies to show that…

Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…

We present a new method for describing quantum measurements in relativistic systems that applies (i) to any QFT and for any field-detector coupling, (ii) to the measurement of any observable, and (iii) to arbitrary size, shape and motion of…

We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an…

We generalize Blumberg-Mandell's K-theoretic Poitou-Tate duality to arithmetic schemes of arbitrary dimension, smooth and proper over S-integers. As in our earlier papers on the subject, we discuss how to model the compactly supported side…