Ergodic H^1 is not a dual space

Menger probabilistic normed space is a category topological vector space

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

A not on modular hyperconvex space

A Hilbert Space of Stationary Ergodic Processes

Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of datadriven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption, and might be identifiable under severe obfuscation. Our approach is based on uncovering a valid complete inner product on the space of ergodic stationary finite...

bv as a non separable dual space

let c be a field of subsets of a set i. also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...

Color Is Not a Metric Space

Using a metric feature space for pattern recognition, data mining, and machine learning greatly simplifies the mathematics because distances are preserved under rotation and translation in feature space. A metric space also provides a “ruler”, or absolute measure of how different two feature vectors are. In the computer vision community color can easily be misstreated as a metric distance. This...