分離原理及其應用

Wei-Han Lu; 陸韋翰

請用此 Handle URI 來引用此文件： http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2536

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DC 欄位	值	語言
dc.contributor.advisor	劉豐哲
dc.contributor.author	Wei-Han Lu	en
dc.contributor.author	陸韋翰	zh_TW
dc.date.accessioned	2021-05-13T06:41:38Z	-
dc.date.available	2017-07-13
dc.date.available	2021-05-13T06:41:38Z	-
dc.date.copyright	2017-07-13
dc.date.issued	2017
dc.date.submitted	2017-06-16
dc.identifier.citation	{1} Agnew, R.P. and A.P. Morse, {it Extension of linear functionals, with application to limits, integrals, measures, and demsities}, An. Math. 39(1938) 20-30. {2} Banach, S. {it Sur le problème de la mesure}, Fund. Math. 4(1923), 7-33. {3} ------, {it Théorie des opérations linéaires}, Warszawa, 1932, 27. {4} Day, M.M. {it Means on semigroups and groups}, Bull. Amer. Math. Soc. 55(1949), 1054. {5} ------, {it Amenable groups}, Bull. Amer. Math. Soc. 56(1950), 46. {6} ------, {it Amenable semigroups}, Illinois J. Math. 1(1957), 509-544. {7} Greenleaf, Frederick P. {it Invariant Means on Topological Groups}, New York University(1969). {8} Hahn, H. {it Über lineare Gleichungssysteme in linearen Räumen}, J. Reine. Angew. Math. 157(1927), 214-229. {9} Higgins, P.J. {it An Introduction to Topological Groups}, Cambridge University Press(1974). {10} Lax, Peter D. {it Functional Analysis}, Wiley Interscience, New York(2002). {11} Liu, F.C. {it Measure solutions of systems of ineqyalities}, Topol. Methods Nonlinear Anal. 2(1993), 317-331. {12} ------, {it Mazur-Orlicz equality}, Studia Math. 101(2008), 53-63. {13} ------, {it Real Analysis}, Oxford Graduate Texts in Mathematics No.26(2016). {14} Von Neumann, J. {it Zur allgemeinen Theorie des Masses}, Fund. Math. 13(1929), 73-116.
dc.identifier.uri	http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/2536	-
dc.description.abstract	此論文研究一個可推得Hahn-Banach等相關定理的分離原理的等價定理。由此，我們為Agnew-Morse定理、交換群上的順從性、Haar integral的存在性提供自然簡潔的證明。可想像的是這個方法也能幫助分析上其他相關的結果。	zh_TW
dc.description.abstract	This thesis studies an analytic variant of a well-known separation principle from which follows Hahn-Banach theorem and many basic theorems in convex analysis. By using this analytic variant, we provide natural and elegant proofs for Agnew-Morse Theorem, the amenability of abelian groups, and the existence of Haar integrals. It is conceivable that the approach we suggest here might lead to clarification of some results in convex analysis.	en
dc.description.provenance	Made available in DSpace on 2021-05-13T06:41:38Z (GMT). No. of bitstreams: 1 ntu-106-R04221022-1.pdf: 441476 bytes, checksum: 40c3062faca680055bf15ab18bc31e31 (MD5) Previous issue date: 2017	en
dc.description.tableofcontents	1. Introduction and preliminary definitions------------------1 2. The main theorem------------------------------------------4 3. Applications---------------------------------------------13 4. Miscellaneous remarks------------------------------------37 5. References-----------------------------------------------41
dc.language.iso	en
dc.subject	線性算子	zh_TW
dc.subject	泛涵	zh_TW
dc.subject	分離原理	zh_TW
dc.subject	functional analysis	en
dc.subject	linear functional	en
dc.subject	separation principle	en
dc.title	分離原理及其應用	zh_TW
dc.title	A separation principle and its applications	en
dc.type	Thesis
dc.date.schoolyear	105-2
dc.description.degree	碩士
dc.contributor.oralexamcommittee	張志豪,陳俊全
dc.subject.keyword	分離原理,泛涵,線性算子,	zh_TW
dc.subject.keyword	separation principle,functional analysis,linear functional,	en
dc.relation.page	42
dc.identifier.doi	10.6342/NTU201700955
dc.rights.note	同意授權(全球公開)
dc.date.accepted	2017-06-16
dc.contributor.author-college	理學院	zh_TW
dc.contributor.author-dept	數學研究所	zh_TW
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