Related papers: Surface measures in infinite dimension
On the infinite dimensional space $E$ of continuous paths from $[0,1]$ to $\mathbb R^n$, $n \ge 3$, endowed with the Wiener measure $\mu$, we construct a surface measure defined on level sets of the $L^2$-norm of $n$-dimensional processes…
This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…
In this paper, we consider convex sets $K_r = \{g \ge r\}$ in an infinite dimensional Hilbert space, where $g$ is suitably related to a reference Gaussian measure $\mu$ in $H$. We first show how to define a surface measure on the level sets…
Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space, and properties of generated $\sigma$-ideals are studied. These $\sigma$-ideals naturally appear in the differentiation theory and in the abstract…
In this article, we show that every centered Gaussian measure on an infinite dimensional separable Fr\'{e}chet space $X$ over $\mathbb R$ admits some full measure Banach intermediate space between $X$ and its Cameron-Martin space. We…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a…
In Euclidean space, the integration by parts formula for a set of finite perimeter is expressed by the integration with respect to a type of surface measure. According to geometric measure theory, this surface measure is realized by the…
We propose in this short note a prime numbers-based method for constructing probability measures on infinite-dimensional Banach spaces annihilating all finite-dimensional subspaces, supplementing the methods of construction of Gaussian…
The space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By…
We study points of density 1/2 of sets of finite perimeter in infinite-dimensional Gaussian spaces and prove that, as in the finite-dimensional theory, the surface measure is concentrated on this class of points. Here density 1/2 is…
Using finite difference operators, we define a notion of boundary and surface measure for configuration sets under Poisson measures. A Margulis-Russo type identity and a co-area formula are stated with applications to deviation inequalities…
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…
We prove an analogue of the Cauchy integral theorem for hyperholomorphic functions given in three-dimensional domains with non piece-smooth boundaries and taking values in an arbitrary finite-dimensional commutative associative Banach…
We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in non-Archimedean…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
The main result says that every surjective isometry between two ideal Banach function spaces satisfying certain conditions can be presented as a composition of a measurable transformation of a variable and multiplication by a function.
We show that strictly convex surfaces expanding by the inverse Gauss curvature flow converge to infinity in finite time. After appropriate rescaling, they converge to spheres. We describe the algorithm to find our main test function.
We study Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral quartic in momenta. The main results of the work are local description of such metrics in terms of…