The first proof of this theorem was given by Dirichlet in his lectures of 1862 (published 1904) before Heine proved it in 1872. Dugac shows that Dirichlet used the idea of a covering and a finite subcovering more explicitly than Heine. This idea was also used by Weierstrass and Pincherle . Borel formulated his theorem for countable coverings in 1895 and Schönflies and Lebesgue generalized it to any type of covering in 1900 and 1898 (published 1904), respectively. Dugac shows that the story is in fact much more complicated and includes names such as Cousin, Thomae, Young, Vieillefond, Lindelöf .
Ang unang patunay ng teorama na ito ay ibinigay sa pamamagitan ng sa Dirichlet kanyang lektura ng 1862 (Publish 1904) bago Heine proved ito sa 1872. Dugac ay nagpapakita na ang Dirichlet ginamit ang mga ideya ng isang takip at isang wakas subcovering more explicitly kaysa sa Heine. Ideya na ito ay ginagamit din sa pamamagitan ng Weierstrass at Pincherle. Borel formulated kanyang teorama para sa countable coverings sa 1895 at Schönflies at Lebesgue pangkalahatan ito sa anumang uri ng takip sa 1900 at 1898 (Publish 1904), ayon sa. Dugac ay nagpapakita na ang kwento ay sa katunayan marami pa kumplikado at kabilang ang mga pangalan tulad ng pinsan, Thomae, Young, Vieillefond, Lindelöf.