General information Latest issue Archive Impact factor Subscription Guidelines for authors Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Personal entry: Login: Password: Save password Enter Forgotten password? Register

 Teor. Veroyatnost. i Primenen., 1973, Volume 18, Issue 1, Pages 66–77 (Mi tvp2681) Some general questions of the theory of probability measures in linear spaces.

D. Kh. Mushtari

Kazan

Abstract: In § 1, some questions of the theory of cylindrical measures are considered connected to Sazonov's theorem . $\mathrm B$-space $E$ is said to possess the $\mathrm M-\mathrm O$-property if, for any a.s. converging series $\sum r_n(t)x_n$ (where $r_n(t)$ are the Rademacher functions, $x_n\in E$), the series $\sum\|x_n\|^2$ is also converging. The main result of $§ 1$ is: For the existence of such topology $L_E$ in a separable $\mathrm B$-space $E$ that the class of continuous in $L_E$ characteristic functionals would coincide with the class of Fourier transforms of Radon measures in $E'$, it is necessary (Theorem 1 (B)) that the adjoint space $E'$ would possess the $\mathrm M-\mathrm O$-property, and it is sufficient (Theorem 1 (C)), that $E$ would be realizable as a space of random variables and there would exist a Schauder basis in $E$.
§ 2 deals with some generalizations of converse Minlos' theorem  on nuclearity of a countably-Hilbert space on which every continuous characteristic functional is associated with a Radon measure (condition $M$). This theorem is generalized for Frechet spaces. We give also examples of locally convex non-nuclear spaces, separable or not, satisfying the condition $M$; in the separable case the construction is based on the continuum hypothesis and choice axiom. These examples answer in the affirmative the question of Pietsch  about existence of non-nuclear locally convex separable spaces every bilinear form on which is nuclear. Full text: PDF file (769 kB)

English version:
Theory of Probability and its Applications, 1973, 18:1, 64–75 Bibliographic databases: Citation: D. Kh. Mushtari, “Some general questions of the theory of probability measures in linear spaces.”, Teor. Veroyatnost. i Primenen., 18:1 (1973), 66–77; Theory Probab. Appl., 18:1 (1973), 64–75 Citation in format AMSBIB
\Bibitem{Mus73} \by D.~Kh.~Mushtari \paper Some general questions of the theory of probability measures in linear spaces. \jour Teor. Veroyatnost. i Primenen. \yr 1973 \vol 18 \issue 1 \pages 66--77 \mathnet{http://mi.mathnet.ru/tvp2681} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=344409} \zmath{https://zbmath.org/?q=an:0304.60003} \transl \jour Theory Probab. Appl. \yr 1973 \vol 18 \issue 1 \pages 64--75 \crossref{https://doi.org/10.1137/1118005} 

• http://mi.mathnet.ru/eng/tvp2681
• http://mi.mathnet.ru/eng/tvp/v18/i1/p66

 SHARE: Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. D. Kh. Mushtari, “Nekotorye voprosy teorii dualno-radonovskikh otobrazhenii”, Konstr. teor. funkts. i funkts. anal., 1, Izd-vo Kazanskogo un-ta, Kazan, 1977, 51–53 2. D. Kh. Mushtari, “O prostranstvakh, v kotorykh vypolnyayutsya kriterii tipa Bokhnera i Levi”, Konstr. teor. funkts. i funkts. anal., 2, Izd-vo Kazanskogo un-ta, Kazan, 1979, 69–82 3. D. Kh. Mushtari, “Dostatochnye bokhnerovskie topologii”, Konstr. teor. funkts. i funkts. anal., 3, Izd-vo Kazanskogo un-ta, Kazan, 1981, 64–72 • Contact us: math-net2020_12 [at] mi-ras ru Terms of Use Registration Logotypes © Steklov Mathematical Institute RAS, 2020
{"ft_lang_label":"__label__en","ft_lang_prob":0.68922216,"math_prob":0.89352524,"size":3345,"snap":"2020-45-2020-50","text_gpt3_token_len":1038,"char_repetition_ratio":0.09158935,"word_repetition_ratio":0.07905983,"special_character_ratio":0.28550074,"punctuation_ratio":0.19732937,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.98570067,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90],"im_url_duplicate_count":[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-12-05T22:31:56Z\",\"WARC-Record-ID\":\"<urn:uuid:0587063e-5230-4c95-ade2-d03b35a84d77>\",\"Content-Length\":\"30644\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:03c8f8ad-7124-4faf-a27c-26da723a03aa>\",\"WARC-Concurrent-To\":\"<urn:uuid:ffa68add-027a-4a94-af3b-340fa4c7be9e>\",\"WARC-IP-Address\":\"185.129.147.141\",\"WARC-Target-URI\":\"http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=2681&option_lang=eng\",\"WARC-Payload-Digest\":\"sha1:ZRLONO5IUIUKUPQ7KBLE4FQVD2G3K74E\",\"WARC-Block-Digest\":\"sha1:KYSKPRJAEVD4WSBE2SKXCZ27YUIKDVGW\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-50/CC-MAIN-2020-50_segments_1606141750841.83_warc_CC-MAIN-20201205211729-20201206001729-00639.warc.gz\"}"}