منابع مشابه
A Note on Sets of Finite Perimeter in the Plane
The aim of this paper is to study the minimal perimeter problem for sets containing a fixed set E in R2 in a very general setting, and to give the explicit solution. This Article is Dedicated to Paolo Marcellini on the Occasion of His Sixtieth Birthday
متن کاملSets with Finite H-perimeter and Controlled Normal
In the Heisenberg group, we prove that the boundary of sets with finite H-perimeter and having a bound on the measure theoretic normal is an H-Lipschitz graph. Then we show that if the normal is, on the boundary, the restriction of a continuous mapping, then the boundary is an H-regular surface.
متن کاملComputation of the Perimeter of Measurable Sets via their Covariogram. Applications to Random Sets
The covariogram of a measurable set A ⊂ R is the function gA which to each y ∈ R associates the Lebesgue measure of A ∩ (y + A). This paper proves two formulas. The first equates the directional derivatives at the origin of gA to the directional variations of A. The second equates the average directional derivative at the origin of gA to the perimeter of A. These formulas, previously known with...
متن کاملThe Entropy of Random Finite Sets
We define the Boltzmann-Gibbs entropy of random finite set on a general space X as the integration of logarithm of density function over the space of finite sets of X , where the measure for this integration is the dominating measure over this space. We show that with a unit adjustment term, the same value for entropy can be obtained using the calculus of set integrals which applies integration...
متن کاملStrict Interior Approximation of Sets of Finite Perimeter and Functions of Bounded Variation
It is well known that sets of finite perimeter can be strictly approximated by smooth sets, while, in general, one cannot hope to approximate an open set Ω of finite perimeter in R strictly from within. In this note we show that, nevertheless, the latter type of approximation is possible under the mild hypothesis that the (n−1)-dimensional Hausdorff measure of the topological boundary ∂Ω equals...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 2014
ISSN: 0025-584X
DOI: 10.1002/mana.201300341