1 citations · 1 across the 11 of their papers we have counts for
11 papers
Order bornological spaces and order ultrabornological spaces
Liang Hong
Ordered locally convex spaces is an important classes of spaces in the theory of ordered topological vector spaces just as locally convex spaces in the theory of topological vector…
On the relationship between three classes of operators on Riesz spaces
Liang Hong
Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators.…
Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections
Liang Hong
Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and -complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this…
Law of total probability and Bayes' theorem in Riesz spaces
Liang Hong
This note generalizes the notion of conditional probability to Riesz spaces using the order-theoretic approach. With the aid of this concept, we establish the law of total probabil…
Locally solid topological lattice-ordered groups
Liang Hong
Locally solid Riesz spaces have been widely investigated in the past several decades; but locally solid topological lattice-ordered groups seem to be largely unexplored. The paper…
And-Douglas type characterization of generalized conditional expectations, optional projections and predictable projections
Liang Hong
Generalized conditional expectations, optional projections and predictable projections of stochastic processes play important roles in the general theory of stochastic processes, s…
On order-bounded subsets of locally solid Riesz spaces
Liang Hong
In a topological Riesz space there are two types of bounded subsets: order bounded subsets and topologically bounded subsets. It is natural to ask (1) whether an order bounded subs…
The linear topology associated with weak convergence of probability measures
Liang Hong
This expository note aims at illustrating weak convergence of probability measures from a broader view than a previously published paper. Though the results are standard for functi…
On the interpolation property and dominated decomposition property of quasimartingales
Liang Hong
For a quasimartingale majorized by another quasimartingale, it is natural to ask whether a third quasimartingale can be inserted between them. In this paper, we give an affirmative…
Weak convergence of probability measures: a topological vector space point of view
Liang Hong
Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probabili…
On the Riesz decomposition property and the interpolation property of stopping times
Liang Hong
It is known that random variables have the Riesz decomposition property and the interpolation property. These properties are not only interesting in their own rights; they have bee…