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real1.pdf

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# link_1hu8nipzwl6.pdf ## Metadata - PDFFormatVersion=1.2 - IsLinearized=false - IsAcroFormPresent=false - IsXFAPresent=false - IsCollectionPresent=false - IsSignaturesPresent=false - Creator=TeX - Producer=pdfTeX-0.13d - CreationDate=D:20030919113200 ## Contents ### Page 1 2003REAL ANALYSIS Spring 2003SOLUTIONS TO SOME PROBLEMSWarning:These solutions may contain errors!!PREPARED BY SULEYMAN ULUSOYPROBLEM 1. Suppose fn : X → [0, ∞] is measurable for n = 1, 2, 3, ...;f1 ≥ f2 ≥ f3 ≥ ... ≥ 0; fn(x) → f (x) as n → ∞, for every x ∈ X . a)Give a counterexample to show that we do not have generall

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