Every separable Banach space is isometric to a space of continuous nowhere differentiable functions
نویسندگان
چکیده
منابع مشابه
Everywhere Continuous Nowhere Differentiable Functions
Here I discuss the use of everywhere continuous nowhere differentiable functions, as well as the proof of an example of such a function. First, I will explain why the existence of such functions is not intuitive, thus providing significance to the construction and explanation of these functions. Then, I will provide a specific detailed example along with the proof for why it meets the requireme...
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The title above is wrong, because the strong dual of a Banach space is too strong to assert that the natural correspondence between a space and its bidual is an isomorphism. This, from a categorical point of view, is indeed the right duality concept because it yields a self adjoint dualisation functor. However, for many applications the non–reflexiveness problem can be solved by replacing the n...
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Let C be the space of all real-valued continuous functions defined on the unit interval provided with the uniform norm. In the Scottish Book, Banach raised the question of the descriptive class of the subset D of C consisting of all functions which are differentiable at each point of [0,1]. Banach pointed out that D forms a coanalytic subset of C and asked whether D is a Borel set. Later Mazurk...
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In the space of continuous functions of a real variable, the set of nowhere dilferentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a measure theoretic sense (which is different from Wiener measure), "almost every" continuous function is nowhere dilferentiable. Similar results concerning other types of regularity, such as Holder cont...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1995-1328375-8