Fields of sets, set functions, set function integrals, and finite additivity.
Geometric expansion, Lyapunov exponents and foliations
Geometrische Bedingungen für die Integrabilität von Vektor-Feldern auf Teilmengen.
Hake's property of a multidimensional generalized Riemann integral
Hausdorff measures of the set of critical values of functions of the class
Hyperlogarithmic expansion and the volume of a hyperbolic simplex
Inequalities for Jacobians: interpolation techniques
Inverse Function Theorems and Jacobians over Metric Spaces
We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.
Inverse mean value property of harmonic functions.
Iterated quasi-arithmetic mean-type mappings
We work with a fixed N-tuple of quasi-arithmetic means generated by an N-tuple of continuous monotone functions (I an interval) satisfying certain regularity conditions. It is known [initially Gauss, later Gustin, Borwein, Toader, Lehmer, Schoenberg, Foster, Philips et al.] that the iterations of the mapping tend pointwise to a mapping having values on the diagonal of . Each of [all equal] coordinates of the limit is a new mean, called the Gaussian product of the means taken on b. We effectively...
Multidimensional extension of L. C. Young's inequality.
Multiple integrals evaluated by functional equations
Multiple Lebesgue integration on time scales.
Note on generalized multiple Perron integral
On Mawhin's approach to multiple nonabsolutely convergent integral
On the 1/2 Problem of Besicovitch: quasi-arcs do not contain sharp saw-teeth.
In this paper we give an alternative proof of our recent result that totally unrectifiable 1-sets which satisfy a measure-theoretic flatness condition at almost every point and sufficiently small scales, satisfy Besicovitch's 1/2-Conjecture which states that the lower spherical density for totally unrectifiable 1-sets should be bounded above by 1/2 at almost every point. This is in contrast to rectifiable 1-sets which actually possess a density equal to unity at almost every point. Our present method...
On the fundamental group of the fixed points of an unipotent action.
Perron type integration on -dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence
Quantitative Isoperimetric Inequalities on the Real Line
In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown that, in the Gauss space, a set of given measure and almost minimal Gauss boundary measure is necessarily close to be a half-space.Using only geometric tools, we extend their result to all symmetric log-concave measures on the real line. We give sharp quantitative isoperimetric inequalities and prove that among sets of given measure and given asymmetry (distance to half line, i.e. distance to sets of minimal perimeter),...
Riemann average truth-value of Łukasiewicz formulas