A Best Covering Problem.
A class of convex non-coercive functionals and masonry-like materials
A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals
We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.
A covering property of some classes of sets in
A criterion for pure unrectifiability of sets (via universal vector bundle)
Let m,n be positive integers such that m < n and let G(n,m) be the Grassmann manifold of all m-dimensional subspaces of ℝⁿ. For V ∈ G(n,m) let denote the orthogonal projection from ℝⁿ onto V. The following characterization of purely unrectifiable sets holds. Let A be an -measurable subset of ℝⁿ with . Then A is purely m-unrectifiable if and only if there exists a null subset Z of the universal bundle such that, for all P ∈ A, one has . One can replace “for all P ∈ A” by “for -a.e. P ∈...
A generalised conical density theorem for unrectifiable sets.
A Geometric Theory of Surface Area.
A Geometric Theory of Surface Area.
A Geometric Theory of Surface Area. III.
A Non-Probabilistic Proof of the Assouad Embedding Theorem with Bounds on the Dimension
We give a non-probabilistic proof of a theorem of Naor and Neiman that asserts that if (E, d) is a doubling metric space, there is an integer N > 0, depending only on the metric doubling constant, such that for each exponent α ∈ (1/2; 1), one can find a bilipschitz mapping F = (E; dα ) ⃗ ℝ RN.
A note on equivalent interval covering systems for Hausdorff dimension on R.
A Note on Measurable Sets
A note on weak approximation of minors
A problem of invariance for Lebesgue measure
A quantitative version of the isoperimetric inequality : the anisotropic case
We state and prove a stability result for the anisotropic version of the isoperimetric inequality. Namely if is a set with small anisotropic isoperimetric deficit, then is “close” to the Wulff shape set.
A rough curvature-dimension condition for metric measure spaces
We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as...
A Sard type theorem for Borel mappings
We find a condition for a Borel mapping which implies that the Hausdorff dimension of is less than or equal to m-n for almost all .
A set of infinite measure whose ratio set does not contain a given sequence.
Acknowledgement of priority: Second derivates of convex functions.
Addition linearer Cantormengen