WebJan 12, 2000 · The formalism of these analyses is connected with Caratheodory's [12] theorem for Pfaff's [13] equations, introducing the concept of an integral factor for this equation, which inverse was called ... Web这一节单独介绍 Caratheodory 测度扩张定理的证明。这个定理把前面讲涉及到的测度构造技术抽象出来，提供一个构造一般测度的方法。 令 \mathcal A_0 为一代数，不一定是 …

Constantin Carathéodory and the axiomatic …

WebThis is an extremely powerful result of measure theory, and leads, for example, to the Lebesgue measure . The theorem is also sometimes known as the Carathéodory– Fréchet extension theorem, the Carathéodory– Hopf extension theorem, the Hopf extension theorem and the Hahn – Kolmogorov extension theorem. Web在复分析中, Borel–Carathéodory 定理 一般指以下用于估计解析函数幂级数系数的工具: 定理 0.1 (Borel–Carathéodory). 若 h(z) 在包含 ∣z∣ ≤ R 的开集内解析满足 h(0) = 0, 当存在 M > … mark thieroff

Caratheodory

WebConstantin Carathéodory, (born September 13, 1873, Berlin, Germany—died February 2, 1950, Munich), German mathematician of Greek origin who made important contributions to the theory of real … WebConstantin Carathéodory (Greek: Κωνσταντίνος Καραθεοδωρή, romanized: Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He made significant contributions to real and complex analysis, the calculus of variations, and measure theory. He also created … Web测度是欧氏空间中 "长度"、"面积", "体积" 等概念的推广. 在 \mathbb{R}^3 中, 为了建立体积的概念, 也就是说给 \mathbb{R}^3 的每一个子集赋予一个体积, 我们希望找到一个函数 \mathcal{V}, 它给 \mathbb{R}^3 的每一个子集指定一个数 \mathcal{V}(E)\in[0,\infty].为了使得建立的体积概念与我们通常对体积的直觉相吻合 ... mark thierman tucson az