A Proof of Fatou’s Interpolation Theorem
نویسندگان
چکیده
For Fatou’s interpolation theorem of 1906 we suggest a new elementary proof.
منابع مشابه
Another proof of Banaschewski's surjection theorem
We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...
متن کاملAn Institution-independent Proof of Craig Interpolation Theorem
We formulate a general institution-independent (i.e. independent of the details of the actual logic formalised as institution) version of the Craig Interpolation Theorem and prove it in dependence of Birkhoff-style axiomatizability properties of the actual logic. We formalise Birkhoff-style axiomatizability within the general abstract model theoretic framework of institution theory by the novel...
متن کاملProof of Theorem A
Since the full proof of this theorem 10] is simple yet quite tedious, we connne ourselves to the guidelines of the proof. Observing the angles between the three sample points s i ; s j ; s k forming the minimal angle and the corresponding VD vertex v, we take advantage of the fact that d(v; s i) < d(s i ; s k) (Theorem 4.2(ii)) and, by trigonometric arguments, show that sin sin(120) R M
متن کاملA new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملMechanising a Proof of Craig's Interpolation Theorem for Intuitionistic Logic in Nominal Isabelle
Craig’s Interpolation Theorem is an important meta-theoretical result for several logics. Here we describe a formalisation of the result for first-order intuitionistic logic without function symbols or equality, with the intention of giving insight into how other such results in proof theory might be mechanically verified, notable cut-admissibility. We use the package Nominal Isabelle, which ea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2022
ISSN: ['1531-5851', '1069-5869']
DOI: https://doi.org/10.1007/s00041-022-09936-4