On the individual ergodic theorem on a logic
Outer and inner vanishing measures and division in H∞ + C.
Measures on the unit circle are well studied from the view of Fourier analysis. In this paper, we investigate measures from the view of Poisson integrals and of divisibility of singular inner functions in H∞ + C. Especially, we study singular measures which have outer and inner vanishing measures. It is given two decompositions of a singular positive measure. As applications, it is studied division theorems in H∞ + C.
Pairwise Borel and Baire measures in bispaces
In this paper we continue the study of the concepts of pairwise Borel and Baire measures in a bispace, recently introduced in [10]. We investigate some of its consequences including the problem of a pairwise regular Borel extension of a pairwise Baire measure.
Projective limits of perfect measure spaces
Radon Measures on Banach Spaces with their Weak Topologies
The main concern of this paper is to present some improvements to results on the existence or non-existence of countably additive Borel measures that are not Radon measures on Banach spaces taken with their weak topologies, on the standard axioms (ZFC) of set-theory. However, to put the results in perspective we shall need to say something about consistency results concerning measurable cardinals.
Riesz spaces of measures on semirings
The Bochner-Kolmogorov extension theorem for semispectral measures
The symmetric Choquet integral with respect to Riesz-space-valued capacities
A definition of “Šipoš integral” is given, similarly to [3],[5],[10], for real-valued functions and with respect to Dedekind complete Riesz-space-valued “capacities”. A comparison of Choquet and Šipoš-type integrals is given, and some fundamental properties and some convergence theorems for the Šipoš integral are proved.
The Zero-one law for Products of Internal *-finitely Additive Probabiltty Spaces
Which moments of a logarithmic derivative imply quasiinvariance.