existence of the Lebesgue measure

Theorem (Lebesgue).

Let $\\mathcal{B}$ be the Borel $\\sigma$ -algebra (http://planetmath.org/BorelSigmaAlgebra) on the real number line. Then, there is a unique measure $\\mu$ on the measurable space $(\\mathbb{R},\\mathcal{B})$ satisfying

\\mu\\left((a,b)\\right)=b-a

for all real numbers $a<b$ .

随便看

ProofOfTheUniformizationTheorem
proof of the uniformization theorem
ProofOfTheWeakNullstellensatz
proof of the weak Nullstellensatz
ProofOfTheWellfoundedInductionPrinciple
proof of the well-founded induction principle
ProofOfThirdIsomorphismTheorem
proof of third isomorphism theorem
ProofOfThuesLemma
proof of Thue’s Lemma
ProofOfTietzeExtensionTheorem
proof of Tietze extension theorem
ProofOfTopologicallyIrreducibleRepresentationsAreAlgebraicallyIrreducibleForCalgebras
proof of topologically irreducible representations are algebraically irreducible for C^*-algebras
ProofOfTranscendentalRootTheorem
proof of transcendental root theorem
ProofOfTriangleIncenter
proof of triangle incenter
ProofOfTrigonometricVersionOfCevasTheorem
proof of trigonometric version of Ceva’s theorem
ProofOfTukeysLemma
proof of Tukey’s lemma
ProofOfTuransTheorem
proof of Turan’s theorem
ProofOfTychonoffsTheorem

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。