-distance sets, Falconer conjecture, and discrete analogs.
Kadec norms and Borel sets in a Banach space
We introduce a property for a couple of topologies that allows us to give simple proofs of some classic results about Borel sets in Banach spaces by Edgar, Schachermayer and Talagrand as well as some new results. We characterize the existence of Kadec type renormings in the spirit of the new results for LUR spaces by Moltó, Orihuela and Troyanski.
K-analytic locally convex spaces
Kapazitäten und obere Einhüllende von Maßen.
Kelly's theorem from the duality of LP and Tychonoff's theorem
Kolam indiens, dessins sur le sable aux îles Vanuatu, courbe de Sierpinski et morphismes de monoïde
Nous montrons que le tracé d’un kolam indien classique, que l’on retrouve aussi dans la tradition des dessins sur le sable aux îles Vanuatu, peut être engendré par un morphisme de monoïde. La suite infinie morphique ainsi obtenue est reliée à la célèbre suite de Prouhet-Thue-Morse, mais elle n’est -automatique pour aucun entier .
Kolmogoroff consistency theorem for Gleason measures
Konvergenzsaetze fur ein voll Daniell-integral
KPZ formula for log-infinitely divisible multifractal random measures
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. Comm. Math. Phys. 236 (2003) 449–475]. If M is a non degenerate multifractal measure with associated metric ρ(x,y) = M([x,y]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dimH of a measurable set K and the Hausdorff dimension dimHρ with respect to ρ of the same set: ζ(dimHρ(K)) = dimH(K). Our results can...
KPZ formula for log-infinitely divisible multifractal random measures
We consider the continuous model of log-infinitely divisible multifractal random measures (MRM) introduced in [E. Bacry et al. Comm. Math. Phys.236 (2003) 449–475]. If M is a non degenerate multifractal measure with associated metric ρ(x,y) = M([x,y]) and structure function ζ, we show that we have the following relation between the (Euclidian) Hausdorff dimension dimH of a measurable set K and the Hausdorff dimension dimHρ with respect to ρ of the same set: ζ(dimHρ(K)) = dimH(K). Our results can...
Kurepa's Hypothesis and a Problem of Ulam on Families of Measures.
Kurzweil’s PU integral as the Lebesgue integral
For a merely continuous partition of unity the PU integral is the Lebesgue integral.
Kvadratura kruhu ve dvacátém století
-continuous partitions of unity on normed spaces
-improving properties of measures of positive energy dimension
A measure is called -improving if it acts by convolution as a bounded operator from to for some q > p. Positive measures which are -improving are known to have positive Hausdorff dimension. We extend this result to complex -improving measures and show that even their energy dimension is positive. Measures of positive energy dimension are seen to be the Lipschitz measures and are characterized in terms of their improving behaviour on a subset of -functions.
-непрерывные селекторы неподвижных точек многозначных отображений с разложимыми значениями. I: Теоремы существования.
-Непрерывные селекторы неподвижных точек многозначных отображений с разложимыми значениями. II. Теоремы релаксации
-spectrum of the Bernoulli convolution associated with the golden ratio
Based on a set of higher order self-similar identities for the Bernoulli convolution measure for (√5-1)/2 given by Strichartz et al., we derive a formula for the -spectrum, q >0, of the measure. This formula is the first obtained in the case where the open set condition does not hold.
La continuité de la section d'un ensemble semi-analytique et compact
La convergence presque sûre des moyennes ergodiques suivant certaines sous-suites d'entiers