Related papers: James' weak compactness theorem: an exposition
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…
We study the detection capability of the weak-value amplification on the basis of the statistical hypothesis testing. We propose a reasonable testing method in the physical and statistical senses to find that the weak measurement with the…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
Under no additional assumptions, in this paper we construct a Ramsey expansion for every category of finite objects with finite small Ramsey degrees. Our construction is based on the relationship between small Ramsey degrees, weak…
First, a misconception about the spectrum of a confined particle is evidentiated. Then, the results are shown to be incorrect by means of a counter-example, an explicit preparation for the probe is given that yields an arbitrary…
In this paper, we generalize weak KAM theorem from positive Lagrangian systems to "proper" Hamilton-Jacobi equations. We introduce an implicitly defined solution semigroup of evolutionary Hamilton-Jacobi equations. By exploring the…
This note describes Fatou's lemma and Lebesgue's dominated convergence theorem for a sequence of measures converging weakly to a finite measure and for a sequence of functions whose negative parts are uniformly integrable with respect to…
The aim of this note is to give a quick algebraic proof of (the combinatorial part of) the classification theorem for compact real surfaces, whose classical proofs (as in the Massey book and in the Conway ZIP proof) are based on surgery…
We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem…
In this paper, inspired by the concept of generalized weakly contractive mappings in metric spaces, we introduce C-Class function and fixed point theory for weakly contractive in the setting of rectangular $b$-metric spaces and established…
We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\omega_1, \omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense…
We prove a compactness result with respect to $\Gamma$-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the…
We prove a multiparameter version of a classical theorem of Jones and Journe on weak-star convergence in the Hardy space $H^1$.
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
In this paper we introduce a notion of tightness for a family of nonlinear expectations and show that the tightness can be applied to obtain weak compactness in a framework of nonlinear expectation space. This criterion is very useful for…
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…