Midterm_Solutions - Mathematics 6320 Midterm Examination...

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Mathematics 6320 NAME Midterm Examination March 10, 2010 This exam consists of 4 problems, numbered 1–4 . For partial credit you must present your work clearly and understandably; no credit will be given for unsupported answers. Please write your name on each page. If more space than allotted is needed, use the back of the previous page and make note of this. Please make your final answer clear by circling it. Except for your name, please refrain from writing anywhere else on this page. During the exam, no calculators, computers, or other electronic aids are allowed, nor are you allowed to refer to any written notes or source material, nor to communicate with other students. Please turn off all cell phones Check this examination booklet before you start. There should be 4 problems on 7 pages (including this one). You have fifty minutes to complete the exam.
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NAME Math 6320 Midterm Examination Page 2 Question Points Score 1 30 2 20 3 30 4 20 Total 100
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NAME Math 6320 Midterm Examination Page 3 1. [30 points] (a) State the monotone convergence theorem. Let f be a measurable function on E , and { f n } a sequence of measurable functions on a measure space ( E, Σ ). If f n % f pointwise a.e. and there exists φ L 1 ( E,dμ ) such that f n φ on E for all n then Z E f n Z E f dμ . OR If f n f pointwise a.e. and there exists φ L 1 ( E,dμ ) such that f n φ on E for all n then Z E f n Z E f dμ . (b) State the dominated convergence theorem.
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This note was uploaded on 09/01/2010 for the course MATHS MA5205 taught by Professor Chuasangkee during the Spring '09 term at National University of Singapore.

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Midterm_Solutions - Mathematics 6320 Midterm Examination...

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