Displaying similar documents to “Products and projective limits of function spaces”

Products of completion regular measures

David Fremlin, S. Grekas (1995)

Fundamenta Mathematicae

Similarity:

We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.

Construction of non-subadditive measures and discretization of Borel measures

Johan Aarnes (1995)

Fundamenta Mathematicae

Similarity:

The main result of the paper provides a method for construction of regular non-subadditive measures in compact Hausdorff spaces. This result is followed by several examples. In the last section it is shown that “discretization” of ordinary measures is possible in the following sense. Given a positive regular Borel measure λ, one may construct a sequence of non-subadditive measures μ n , each of which only takes a finite set of values, and such that μ n converges to λ in the w*-topology. ...

On products of Radon measures

C. Gryllakis, S. Grekas (1999)

Fundamenta Mathematicae

Similarity:

Let X = [ 0 , 1 ] Γ 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 [ 0 , 1 ] F are equivalent to the F-dimensional Lebesgue measure. We generalize this construction to any compact group of weight ≥ c, by replacing the Lebesgue product...