Related papers: Defining the Mean of a Real-Valued Function on an …
Recently Bingbing Liang and Hanfeng Li computed the mean dimension and metric mean dimension for algebraic actions of amenable groups. We show how to extend their computation of metric mean dimension to the case of sofic groups, provided…
By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy $p$-harmonic and $p$-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local…
Robots that interact with humans in a physical space or application need to think about the person's posture, which typically comes from visual sensors like cameras and infra-red. Artificial intelligence and machine learning algorithms use…
Motivated by the well-known implications among $t$-convexity properties of real functions, analogous relations among the upper and lower $M$-convexity properties of real functions are established. More precisely, having an $n$-tuple…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
Whether the goal is to analyze voting behavior, locate facilities, or recommend products, the problem of translating between (ordinal) rankings and (numerical) utilities arises naturally in many contexts. This task is commonly approached by…
Relevance is an underlying concept in the field of Information Science and Retrieval. It is a cognitive notion consisting of several different criteria or dimensions. Theoretical models of relevance allude to interdependence between these…
We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…
We investigate the dynamical property of the naive mean dimension for continuous actions of any countable group on compact metrizable spaces. It is shown that naive mean dimension serves as an upper bound of sofic mean dimension for actions…
This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for $I(1)$ linear processes with moderately large cross-sectional dimension. The approach is based on empirical canonical correlations…
On any metric space, I provide an intrinsic characterization of those complex-valued functions which are uniform limits of Lipschitz functions. There are applications to function theory on complete Riemannian manifolds and, in particular,…
We quickly review and make some comments on the concept of convexity in metric spaces due to Takahashi. Then we introduce a concept of convex structure based convexity to functions on these spaces and refer to it as $W-$convexity.…
This paper proposes a new approach to obtain uniformly valid inference for linear functionals or scalar subvectors of a partially identified parameter defined by linear moment inequalities. The procedure amounts to bootstrapping the value…
These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.
Motivated by Leinster-Cobbold measures of biodiversity, the notion of the spread of a finite metric space is introduced. This is related to Leinster's magnitude of a metric space. Spread is generalized to infinite metric spaces equipped…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
In this work we investigate and characterize linear functionals $L:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}$ with absolutely continuous representing measures $\mu$, i.e., $\mathrm{d}\mu(x) = g(x)\,\mathrm{d} x$ for some density $g$. We focus…
We study the statistical convergence of metric valued sequences and of their subsequences. The interplay between the statistical and usual convergences in metric spaces is also studied.
Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…
The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and…