The Bochner mean square deviation and law of large numbers for squares of random elements in Banach lattices.
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
The Laplace transform of measures on the cone of a vector lattice.
The Minlos lemma for positive-definite functions on additive subgroups of
Let H be a real Hilbert space. It is well known that a positive-definite function φ on H is the Fourier transform of a Radon measure on the dual space if (and only if) φ is continuous in the Sazonov topology (resp. the Gross topology) on H. Let G be an additive subgroup of H and let (resp. ) be the character group endowed with the topology of uniform convergence on precompact (resp. bounded) subsets of G. It is proved that if a positive-definite function φ on G is continuous in the Gross topology,...
The product-decomposability of probability measures on Abelian metrizable groups [Book]
Topological algebras of random elements
Let L₀(Ω;A) be the Fréchet space of Bochner-measurable random variables with values in a unital complex Banach algebra A. We study L₀(Ω;A) as a topological algebra, investigating the notion of spectrum in L₀(Ω;A), the Jacobson radical, ideals, hulls and kernels. Several results on automatic continuity of homomorphisms are developed, including versions of well-known theorems of C. Rickart and B. E. Johnson.
Transportation Cost for Gaussian and Other Product Measures.
Two remarks on the Khintchine-Kahane inequality
Unconditional basic sequences of random variables in Lp(E).
Unconditional convergence of random series and the geometry of Banach spaces.
Une loi de zéro-un pour une classe de mesures sur les groupes
Uniform upper bound for a stable measure of a small ball.
Uniqueness Theorems for Measures in Lr and C0 (...).
Weak and strong moments of random vectors
We discuss a conjecture about comparability of weak and strong moments of log-concave random vectors and show the conjectured inequality for unconditional vectors in normed spaces with a bounded cotype constant.
Wiener integral in the space of sequences of real numbers
Аппроксимация распределений статистик Мизеса с многомерными ядрами.
Вероятностные неравенства для сумм независимых случайных величин со значениями в банаховом пространстве.
Замечание о ряде Г. Крамера
Метод функционального интегрирования в исследовании динамики модельных гамильтонианов
Непрерывность универсально измеримых линейных отображений