Some results for probability measures on linear topological vector spaces with an application to Strassen's log log law

On $beta-$topological vector spaces

We introduce and study a new class of spaces, namely $beta-$topological vector spaces via $beta-$open sets. The relationships among these spaces with some existing spaces are investigated. In addition, some important and useful characterizations of $beta-$topological vector spaces are provided.  

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

Small ball probability estimates for log-concave measures

We establish a small ball probability inequality for isotropic log-concave probability measures: there exist absolute constants c1, c2 > 0 such that if X is an isotropic log-concave random vector in R with ψ2 constant bounded by b and if A is a non-zero n × n matrix, then for every ε ∈ (0, c1) and y ∈ R, P (‖Ax− y‖2 6 ε‖A‖HS) 6 ε ` c2 b ‖A‖HS ‖A‖op ́2 , where c1, c2 > 0 are absolute constants.

Functional Inequalities for Gaussian and Log-Concave Probability Measures

We give three proofs of a functional inequality for the standard Gaussian measure originally due to William Beckner. The first uses the central limit theorem and a tensorial property of the inequality. The second uses the Ornstein-Uhlenbeck semigroup, and the third uses the heat semigroup. These latter two proofs yield a more general inequality than the one Beckner originally proved. We then ge...

Some Results on p-Best Approximation in Vector Spaces