The Hahn-Banach theorem implies the existence of a non-Lebesgue measurable set
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چکیده
منابع مشابه
The Hahn-banach Theorem Implies the Existence of a Non Lebesgue-measurable Set
§0. Introduction. Few methods are known to construct non Lebesgue-measurable sets of reals: most standard ones start from a well-ordering of R, or from the existence of a non-trivial ultrafilter over ω, and thus need the axiom of choice AC or at least the Boolean Prime Ideal theorem BPI (see [5]). In this paper we present a new way for proving the existence of non-measurable sets using a conven...
متن کاملThe Hahn-banach Theorem Implies the Existence of a Non Lebesgue-measureable Set
Few methods are known to construct nonLebesgue-measurable sets of reals: most standard ones start from a well-ordering of R, or from the existence of a non-trivial ultrafilter over ω, and thus need the axiom of choice AC or at least the Boolean Prime Ideal theorem (BPI see [5]). In this paper we present a new way for proving the existence of non-measurable sets using a convenient operation of a...
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was established by Hahn [1; p. 217] in 1927, and independently by Banach [2; p. 212] in 1929, who also generalized Theorem 0 for real spaces, to the situation in which the functional q :E^>R is an arbitrary subadditive, positive homogeneous functional [2; p. 226]. Theorem 0 was not established for complex spaces until 1938, when it was deduced from the real theorem by Bohnenblust and Sobczyk [3...
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The idea behind this article is to provide a unified and relatively nontechnical framework for treating the main existence theorems for continuous linear functionals in functional analysis, convex analysis, Lagrange multiplier theory, and minimax theory. While many of the results in this article are already known, our approach is new, and gives a large number of results with considerable econom...
متن کاملA FUZZY VERSION OF HAHN-BANACH EXTENSION THEOREM
In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1991
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-138-1-13-19