相关论文: A One-Sentence Inverse Image Proof of Lusin's Theo…

We give a one-sentence proof of McLaughlin and Rundell's inverse uniqueness theorem.

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.

This article presents simple and easy proofs of the Implicit Function Theorem and the Inverse Function Theorem, in this order, both of them on a finite-dimensional Euclidean space, that employ only the Intermediate Value Theorem and the…

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

The Bertrand's theorem can be formulated as the solution of an inverse problem for a classical unidimensional motion. We show that the solutions of these problems, if restricted to a given class, can be obtained by solving a numerical…

We give a short, explicit proof of Hindman's Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. We give several exampls of colorings of the integers which do not…

One of the most famous results in Complex Analysis is the Little Picard Theorem, that characterizes the image set of an arbitrary entire function. Specifically, the theorem states that this image set is either the whole complex plane or the…

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

We give a new proof of Lucas' Theorem in elementary number theory.

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

The elegance and usefulness of a complex formulation of the basic lensing equations is demonstrated with a number of applications. Using standard tools of complex function theory, we present, for instance, a new proof of the fact that the…

A very short proof of Kneser's theorem via transversal is given.

We give a "soft" proof of Alberti's Luzin-type theorem in [1] (G. Alberti, A Lusintype theorem for gradients, J. Funct. Anal. 100 (1991)), using elementary geometric measure theory and topology. Applications to the $C^2$-rectifiability…

We give a short and self-contained proof of Levi's Extension Lemma for pseudoline arrangements.

We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…

We present in this work a new and simple proof of the false centre theorem.

In this note we give a detailed proof of a theorem of Aubin.