Constantin Carathéodory

Constantin Carathéodory (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 an axiomatic formulation of thermodynamics. Carathéodory is considered one of the greatest mathematicians of his era and the most renowned Greek mathematician since antiquity. Constantin Carathéodory was born in 1873 in Berlin to Greek parents and grew up in Brussels. His father tr, a lawyer, served as the Ottoman ambassador to Belgium, St. Petersburg and Berlin. His mother, Despina, née Petrokokkinos, was from the island of Chios. The Carathéodory family, originally from Bosnochori or Vyssa, was well established and respected in Constantinople, and its members held many important governmental positions. The Carathéodory family spent 1874–75 in Constantinople, where Constantin's paternal grandfather lived, while his father Stephanos was on leave. Then in 1875 they went to Brussels when Stephanos was appointed there as Ottoman Ambassador. In Brussels, Constantin's younger sister Julia was born. The year 1879 was a tragic one for the family since Constantin's paternal grandfather died in that year, but much more tragically, Constantin's mother Despina died of pneumonia in Cannes. Constantin's maternal grandmother took on the task of bringing up Constantin and Julia in his father's home in Belgium. They employed a German maid who taught the children to speak German. Constantin was already bilingual in French and Greek by this time. Constantin began his formal schooling at a private school in Vanderstock in 1881. He left after two years and then spent time with his father on a visit to Berlin, and also spent the winters of 1883–84 and 1884–85 on the Italian Riviera. Back in Brussels in 1885 he attended a grammar school for a year where he first began to become interested in mathematics.

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MATH-303: Measure and integration

Dans ce cours on définira et étudiera la notion de mesure et d'intégrale contre une mesure dans un cadre général, généralisant ce qui a été fait en Analyse IV dans le cas réel. On verra aussi quelques

Towards self-consistent plasma modelisation in presence of neoclassical tearing mode and sawteeth: effects on transport coefficients

Olivier Sauter, Antoine Pierre Emmanuel Alexis Merle

The neoclassical tearing modes (NTM) increase the effective heat and particle radial transport inside the plasma, leading to a flattening of the electron and ion temperature and density profiles at a given location depending on the safety factor q rational ...

2017

Asymptotic linearity and Hadamard differentiability

Charles Stuart

For a mapping between Banach spaces, two weaker variants of the usual notion of asymptotic linearity are defined and explored. It is shown that, under inversion through the unit sphere, they correspond to Hadamard and weak Hadamard differentiability at the ...

2012

We develop an axiomatic approach to the theory of Sobolev spaces on metric measure spaces and we show that this axiomatic construction covers the main known examples (Hajlasz Sobolev spaces, weighted Sobolev spaces, Upper-radients, etc). We then introduce ...

2001

Greek diaspora

The Greek diaspora, also known as Omogenia (Omogéneia), are the communities of Greeks living outside of Greece and Cyprus (excluding Northern Cyprus). Such places historically include Albania, North Macedonia, parts of the Balkans, southern Russia, Ukraine, Asia Minor, Sudan, the region of Pontus, Eastern Anatolia, Georgia, the South Caucasus, Egypt, southern Italy, and Cargèse in Corsica. The term also refers to communities established by Greek migration outside of these traditional areas; such as in Australia, Chile, Canada and the United States.

Outer measure

In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures.

Greek mathematics

Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly attested from the late 7th century BC to the 6th century AD, around the shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire region, from Anatolia to Italy and North Africa, but were united by Greek culture and the Greek language. The development of mathematics as a theoretical discipline and the use of proofs is an important difference between Greek mathematics and those of preceding civilizations.

Integer Cones MATH-504: Integer optimisation

Covers the concept of integer cones and Carathéodory's theorem with illustrative examples.

Carathéodory's Theorem and Dimension Bound MATH-513: Metric embeddings

Explores Carathéodory's Theorem and its dimension implications for set representation.

Probability Measures and Random Variables MATH-432: Probability theory

Covers the Caratheodory extension theorem, uniqueness and existence of probability measures, Bernoulli random variables, and spaces of random variables.