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Egorov worked on triply orthogonal systems and potential surfaces, making a major contribution to differential geometry. Some of Egorov's work was presented by Darboux in his famous four volume work Lecons sur la théorie général des surfaces et les applications géométriques du calcul infinitésimal .
Egorov also worked on integral equations and a theorem in the theory of functions of a real variable is named after him. Luzin was a member of the school Egorov created in Moscow dealing with functions of a real variable.
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