1. This is used to show existence theorems for holomorphic functions. 2. Dixon s proof used the Existence Theorem of Partha Dasgupta and Eric Maskin. 3. The existence of parallel transport follows from standard existence theorems for ordinary differential equations. 4. The Model Existence Theorem and its proof can be formalized in the framework of Peano arithmetic. 5. The crucial Takagi existence theorem was known by 1920 and all the main results by about 1930. 6. When " F " is single valued, this is the classic Peano existence theorem . 7. The actual isomorphism used and the existence theorem is described in the theory of the norm residue symbol. 8. This theorem can be considered as an existence theorem : any stationary process has this seemingly special representation. 9. However, this existence theorem is purely theoretical, as such a base has never been explicitly described. 10. An even more general result is the Carath�odory existence theorem , which proves existence for some discontinuous functions ?.
