Instruct: Given a premise, retrieve a hypothesis that is entailed by the premise.
Query: In mathematics, the Vitali–Carathéodory theorem is a result in real analysis that shows that, under the conditions stated below, integrable functions can be approximated in L from above and below by lower- and upper-semicontinuous functions, respectively. It is named after Giuseppe Vitali and Constantin Carathéodory.
the Vitali–Carathéodory theorem is a solution in real analysis 
Giuseppe Vitali and Constantin Carathéodory are related

 the Vitali–Carathéodory theorem was developed by a Norwegian 
Giuseppe Vitali and Constantin Carathéodory were partners
Giuseppe Vitali and Constantin Carathéodory knew each other
Giuseppe Vitali and Constantin Carathéodory could solve this theorem.
Giuseppe Vitali and Constantin Carathéodory would understand this statement if they read it.
Giuseppe Vitali and Constantin Carathéodory are both accomplished mathematicians.
Giuseppe Vitali and Constantin Carathéodory were bitter rivals
Giuseppe Vitali and Constantin Carathéodory shared credit for discovering this theorem, which is why it's named for them.
Giuseppe Vitali was 18 when he came up with the theorem
The author feels that the term assures that a limit is respected.
The author feels that the limit in question is respected.
Before the Risch algorithm indefinite integration was impossible.
A series of numbers has been presented in this context
Pavel Sergeyevich Alexandrov made contributions to set theory and topology.
Pavel Alexandrov did topological math
The Krylov–Bogolyubov averaging method was first used by a man
Topology was extended by Alexandrov.
Aleksandrov's research was considered important and advanced knowledge of set theory and topology.
In topological math, the Aleandroff extension extends space
Before the Risch algorithm computers had a hard time finding antiderivatives.
 the Vitali–Carathéodory theorem was invented by Charles Dugal
 the Vitali–Carathéodory theorem does not involve any addition
Giuseppe Vitali and Constantin Carathéodory are related
