Weakly compactly generated Frechet spaces.
Weakly mixing transformations and the Carathéodory definition of measurable sets
Let 𝕋 denote the set of complex numbers of modulus 1. Let v ∈ 𝕋, v not a root of unity, and let T: 𝕋 → 𝕋 be the transformation on 𝕋 given by T(z) = vz. It is known that the problem of calculating the outer measure of a T-invariant set leads to a condition which formally has a close resemblance to Carathéodory's definition of a measurable set. In ergodic theory terms, T is not weakly mixing. Now there is an example, due to Kakutani, of a transformation ψ̃ which is weakly mixing but not strongly...
Weakly tight functions and their decomposition.
Weakly α-favourable measure spaces
I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.
Weak-star continuous homomorphisms and a decomposition of orthogonal measures
We consider the set of complex-valued homomorphisms of a uniform algebra which are weak-star continuous with respect to a fixed measure . The -parts of are defined, and a decomposition theorem for measures in is obtained, in which constituent summands are mutually absolutely continuous with respect to representing measures. The set is studied for -invariant algebras on compact subsets of the complex plane and also for the infinite polydisc algebra.
Weighted Csiszár-Kullback-Pinsker inequalities and applications to transportation inequalities
Weighted integral inequalities for the nontangential maximal function, Lusin area integral, and Walsh-Paley series
Weighted multiplicative integral inequalities.
Weighted norm inequalities relating the and the area functions
Well-posedness and fractals via fixed point theory.
What’s the price of a nonmeasurable set?
In this note, we prove that the countable compactness of together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of . This is done by providing a family of nonmeasurable subsets of whose intersection with every non-negligible Lebesgue measurable set is still not Lebesgue measurable. We develop this note in three sections: the first presents the main result, the second recalls known results concerning non-Lebesgue measurability and its relations with the Axiom...
When ℵ₁ many sets are contained in a countably generated σ-field
We discuss the problem when ℵ₁ sets are contained in a σ-generated σ-field on some set X. This is related to a problem raised by K. P. S. Bhaskara Rao and Rae Michael Shortt [Dissertationes Math. 372 (1998)] which we answer. We also briefly discuss generating the family of all subsets from rectangles.
When is the union of an increasing family of null sets?
We study the problem in the title and show that it is equivalent to the fact that every set of reals is an increasing union of measurable sets. We also show the relationship of it with Sierpi'nski sets.
Where are typical functions one-to-one?
Suppose is closed. Is it true that the typical (in the sense of Baire category) function in is one-to-one on ? If we show that the answer to this question is yes, though we construct an with for which the answer is no. If is the middle- Cantor set we prove that the answer is yes if and only if There are ’s with Hausdorff dimension one for which the answer is still yes. Some other related results are also presented.
Whitney covers and quasi-isometry of -averaging domains.