-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