Several important multivariate probability inequalities can be formulated in terms of multivariate convolutions of the form ∫ $f_{1}(x)f_{2}(x-\theta )dx$, where ...

For more than 350 years, a mathematics problem whose solution was considered the Holy Grail to the greatest mathematician minds had remained unsolved. Now, a team of mathematicians led by a prominent ...

The minimax inequality $\min_x \sup_y f(x, y) \leqslant \sup_x f(x, x)$, proved by K. Fan for convex spaces, is proved here for certain contractible and acyclic spaces. Some variational inequality and ...

Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...