Related papers: Hasse theorem -- an elementary approach
For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.
We prove a local version of the Mazur-Ulam theorem.
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
This article presents an elementary proof of Zorn's Lemma under the Axiom of Choice, simplifying and supplying necessary details in the original proof by Paul R. Halmos in his book, Naive Set Theory. Also provided, is a preamble to Zorn's…
We propose a simple proof of the vertical half-space theorem for Heisenberg space.
A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
Employing Br\"udern's and Wooley's new complification method, we establish an asymptotic Hasse principle for the number of solutions to a system of r_3 cubic and r_2 quadratic diagonal forms, when the number of cubic equations is at least…
We provide new sufficient conditions under which Ryser's conjecture holds.
We present here a simple and direct proof of the classic geometric version of Hahn-Banach Theorem from its analitic version, in the real case. The reciprocal implication, and the direct proofs of both versions, are already well kown, but…
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…
In this paper, we present a short proof of Halin's grid theorem.
A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.
In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We prove Union-Closed sets conjecture.
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
Conditions for Bayesian posterior robustness have been examined in recent literature. However, many of the proofs seem to be long and complicated. In this paper, we first summarize some basic lemmas that have been applied implicitly or…
We present a theory of lazy imperative timing.
The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas. To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.