Related papers: Proofs for Folklore Theorems on the Radon-Nikodym …
A generalized divergence theorem is established allowing for domains with inner boundaries. The normal trace of a rough integrand is not a Radon measure; rather, the boundary integral is expressed via a surface functional continuous with…
In this note we record a comparison theorem on the B-model variation of semi-infinite Hodge structures. This result is considered a folklore theorem by experts in the field. We only take this opportunity to write it down. Our motivation is…
We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
In this paper, some sufficient conditions for the differentiability of the $n$-variable real-valued function are obtained, which are given based on the differentiability of the $n-1$-variable real-valued function and are weaker than…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
We present and discuss the many results obtained concerning a famous limit theorem, the local limit theorem, which has many interfaces, with Number Theory notably, and for which, in spite of considerable efforts, the question concerning…
In a series of recent works, we have provided a number of explicit expressions for the derivative of the associated Legendre function of the first kind with respect to its degree, $[\partial P_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$, with…
We introduce and study a new family of extensions for the Borsuk-Ulam and topological Radon type theorems. The defining idea for this new family is to replace requirements of the form `a subset that is large in some sense goes to a…
I discuss our current understanding of parton distributions. I begin with the underlying theoretical framework, and the way in which different data sets constrain different partons, highlighting recent developments. The methods of examining…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
By using nonstandard analysis, and in particular iterated hyper-extensions, we give foundations to a peculiar way of manipulating ultrafilters on the natural numbers and their pseudo-sums. The resulting formalism is suitable for…
Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.
There is the classical Radon theorem. Given integer $d \geq 1$ and $d+2$ points in d-dimensional space $R^d$. Then these points can be divided into two disjoint subsets whose convex hulls have a non-empty intersection. The original proof of…
A basic measure of the combinatorial complexity of a convexity space is its Radon number. In this paper we show a fractional Helly theorem for convexity spaces with a bounded Radon number, answering a question of Kalai. As a consequence we…
In this paper we define the Radon-Nikodym class (RN class) of locally convex topological vector spaces. The RN class is characterized in terms of the Radon-Nikodym theorem for vector measures using integrable by seminorm derivatives. It is…
After a review of some of the main results about hyperfinite equivalence relations and their cocycles in the measured setting, we give a definition of a topological AF-equivalence relation. We show that every cocycle is cohomologous to a…
This paper studies the modal logical aspects of provability predicates and consistency statements for theories of arithmetic. First, we provide an overview of previous works on the correspondence between various derivability conditions for…
A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…
We give a survey on recent development of the Novikov conjecture and its applications to topological rigidity and non-rigidity. .