On outer measures and semi-separation of lattices.
On Pettis integrability
Assuming that is a complete probability space and a Banach space, in this paper we investigate the problem of the -inheritance of certain copies of or in the linear space of all [classes of] -valued -weakly measurable Pettis integrable functions equipped with the usual semivariation norm.
On Pettis integral and Radon measures
Assuming the continuum hypothesis, we construct a universally weakly measurable function from [0,1] into a dual of some weakly compactly generated Banach space, which is not Pettis integrable. This (partially) solves a problem posed by Riddle, Saab and Uhl [13]. We prove two results related to Pettis integration in dual Banach spaces. We also contribute to the problem whether it is consistent that every bounded function which is weakly measurable with respect to some Radon measure is Pettis integrable....
On Pettis integrals with separable range
Several techniques have been developed to study Pettis integrability of weakly measurable functions with values in Banach spaces. As shown by M. Talagrand [Ta], it is fruitful to regard a weakly measurable mapping as a pointwise compact set of measurable functions - its Pettis integrability is then a purely measure-theoretic question of an appropriate continuity of a measure. On the other hand, properties of weakly measurable functions can be translated into the language of topological measure theory...
On pointwise ergodic theorems for positive operators
On pointwise limits of sequences of -continuous functions
On Poisson and composed Poisson stochastic set functions
On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II
On possibilistic marginal problem
A possibilistic marginal problem is introduced in a way analogous to probabilistic framework, to address the question of whether or not a common extension exists for a given set of marginal distributions. Similarities and differences between possibilistic and probabilistic marginal problems will be demonstrated, concerning necessary condition and sets of all solutions. The operators of composition will be recalled and we will show how to use them for finding a -product extension. Finally, a necessary...
On Probability Function On Pseudo-Boolean Algebra
On products of admissible liftings and densities.
On products of Radon measures
Let with card Γ ≥ c (c denotes the continuum). We construct two Radon measures μ,ν on X such that there exist open subsets of X × X which are not measurable for the simple outer product measure. Moreover, these measures are strikingly similar to the Lebesgue product measure: for every finite F ⊆ Γ, the projections of μ and ν onto are equivalent to the F-dimensional Lebesgue measure. We generalize this construction to any compact group of weight ≥ c, by replacing the Lebesgue product measure...
On Prohorov spaces
On projection measurability of functions and multifunctions
On projection of nonseparable Souslin and Borel sets along separable spaces
On projective limits of probability spaces
On qualitative cluster sets
On quasi-invariant measures in topological vector spaces.
On Quasi-Invariant Measures in Uniquely Ergodic Systems.
On -dimensional integrals in -space