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In 1919 Radon became assistant professor at Hamburg becoming a full professor in Greifswald in 1922. He taught in Erlangen in 1925, then from 1928 until 1945 he worked at the University of Breslau. He was appointed to the University of Vienna in 1947 and he remained there for the rest of his life.
Radon applied the calculus of variations to differential geometry which led to applications in number theory. He discovered curves whch are now named after him. His best known results involve combining the integration theories of Lebesgue and Stieltjes.
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