Related papers: Convergence in measure under Finite Additivity
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all…
For linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0, 2)$, we study functional convergence of the joint partial sum and partial maxima processes. We derive a…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
We study tightness properties and selective versions of separability in bitopological function spaces endowed with set-open topologies.
The prime objective of this paper is to develop the notion of absolute continuity of functions on a more general setting outside $\R$. For this we have considered a topological space which is a measure space as well. We have built axioms…
The study of local function in topological spaces is remarkable. Various branches have been developed through this study. In this paper, we further consider the local function and exploring the various properties of the same by considering…
The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…
In this paper we study mutual absolute continuity and singularity of probability measures on the path space which are induced by an isotropic stable L\'evy process and the purely discontinuous Girsanov transform of this process. We also…
The Giry monad on the category of measurable spaces sends a space to a space of all probability measures on it. There is also a finitely additive Giry monad in which probability measures are replaced by finitely additive probability…
We examine conditions on a (compact metrizable) space $X$ such that for any space $Y$ and closed subspace $Z$, the set of continuous functions from $Z$ to $X$ which extend to $Y$ is either open or closed in the set of continuous functions…
We give a new characterization of relative entropy, also known as the Kullback-Leibler divergence. We use a number of interesting categories related to probability theory. In particular, we consider a category FinStat where an object is a…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
Let $\mathcal{M}(X,\mathcal{A},\mu)$ be the ring of all real-valued measurable functions constructed over a measure space $(X,\mathcal{A},\mu)$. A topology on $\mathcal{M}(X,\mathcal{A},\mu)$, called the {$F_\mu$-topology} weaker than the {…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
I explain the difficulty of making various concepts of and relating to probability precise, rigorous and physically significant when attempting to apply them in reasoning about objects (e.g., spacetimes) living in infinite-dimensional…
By the additive property, we mean a condition under which $L^p$ spaces over finitely additive measures are complete. Basile and Rao gives a necessary and sufficient condition that a finite sum of finitely additive measures has the additive…
We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…