The relations among the modes of convergence of sequences of measurable functions Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/w66345622

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  • This study undertakes to determine the existence or nonexistence of an implication in either direction between any two out of nine different modes of convergence, with the use of any subset of a set of ten auxiliary hypotheses. The functions are real finite-valued measurable functions defined on an arbitrary abstract measure space. A collection of 25 counterexamples is used to establish the invalidity of the unproved implications. When the desired convergence cannot be concluded, the existence of a convergent subsequence is investigated. An appendix investigates the possible non-uniqueness of the limit function when the definitions of two of the modes are slightly relaxed.
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  • File scanned at 300 ppi (Monochrome) using Capture Perfect 3.0.82 on a Canon DR-9080C in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2010-07-27T18:03:09Z (GMT) No. of bitstreams: 1 CresswellDonaldJay1967.pdf: 1712436 bytes, checksum: db177d2477f77570ea1c3d3c3b4b7e61 (MD5)
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  • description.provenance : Submitted by Nitin Mohan (mohanni@onid.orst.edu) on 2010-07-23T22:46:04Z No. of bitstreams: 1 CresswellDonaldJay1967.pdf: 1712436 bytes, checksum: db177d2477f77570ea1c3d3c3b4b7e61 (MD5)
  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2010-07-27T18:00:57Z (GMT) No. of bitstreams: 1 CresswellDonaldJay1967.pdf: 1712436 bytes, checksum: db177d2477f77570ea1c3d3c3b4b7e61 (MD5)

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