Related papers: On Egorov's Theorem for Infinite Measure
The aim of this paper is to study ultralimits of pointed metric measure spaces (possibly unbounded and having infinite mass). We prove that ultralimits exist under mild assumptions and are consistent with the pointed measured…
An analogue of Gross' logarithmic Sobolev inequality for a class of elements of noncommutative two tori is proved.
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We present a new, elementary, dynamical proof of the prime number theorem.
In this paper the absolute value or distance from the origin analogue of the classical Khintchine-Groshev theorem is established for a single linear form with a `slowly decreasing' error function.
We prove the statement in the title using the connectedness of the interval in real line.
In this note, we will consider an arithmetic analogue of Bogomolov unstability theorem.
We obtain some results related to Romanoff's theorem.
We present an elementary proof of Fermat's Last Theorem. No ancillary results are used, not even the most basic ones. The proof directly leads to a contradiction of the Fermat equation in the set of integers.
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We give a direct proof of the Ohsawa-Takegoshi by solving directly the d-bar equation.
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these…
We study the general moment problem for measures on the real line, with polynomials replaced by more general spaces of entire functions. As a particular case, we describe measures that are uniquely determined by a restriction of their…
In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.
We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also discussed.
We give an alternate proof of three versions of the theorem on extrapolation of Carleson measures.
In this paper we give a new proof for an almost isometry theorem in Alexandrov spaces with curvature bounded below.