Related papers: A simple proof of the Lebesgue decomposition theor…

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We give a simple and short proof of the classical Lebesgue decomposition theorem of measures via the Riesz orthogonal decomposition theorem of Hilbert spaces. The tools we employ are elementary Hilbert space techniques.

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

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

This paper contains a new elementary proof of the Fundamental Theorem of Calculus for the Lebesgue integral. The hardest part of our proof simply concerns the convergence in ${\rm L}^1$ of a certain sequence of step functions, and we prove…

The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces.

A new proof of the decomposition theorem is established using a relation with a version of the local purity theorem of Deligne and Gabber adapted to complex algebraic varieties.

We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.

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

We present a modification of Riesz's construction of the Lebesgue integral, leading directly to finite or infinite integrals, at the same time simplifying the proofs.

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…

The decomposition theorem is deduced from local purity.

The goal of this note is to provide a constructive version of the proof of local structure of etale algebras.

The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.