From sarahwright_34@hotmail.com Tue Nov 2 00:59:08 2004 Return-Path: Received: from XXXXXXXX.XXXXXXX.XXX (root@XXXXXXXX.XXXXXXX.XXX [128.223.142.13]) by XXXX.XXX.XXXXXXXXXX.XXX (8.11.6/8.11.6) with ESMTP id iA26x8w03830 for ; Tue, 2 Nov 2004 00:59:08 -0600 Received: from hotmail.com (bay2-f8.bay2.hotmail.com [65.54.247.8]) by XXXXXXXX.XXXXXXX.XXX (8.12.11/8.12.11) with ESMTP id iA26x7VF003782 for ; Mon, 1 Nov 2004 22:59:07 -0800 (PST) Received: from mail pickup service by hotmail.com with Microsoft SMTPSVC; Mon, 1 Nov 2004 22:59:01 -0800 Received: from 68.121.138.7 by by2fd.bay2.hotmail.msn.com with HTTP; Tue, 02 Nov 2004 06:59:00 GMT X-Originating-IP: [68.121.138.7] X-Originating-Email: [sarahwright_34@hotmail.com] X-Sender: sarahwright_34@hotmail.com From: "Sarah Wright" To: XXX@XXXXXXXX.XXXXXXX.XXX Subject: real Date: Tue, 02 Nov 2004 01:59:00 -0500 Mime-Version: 1.0 Content-Type: text/plain; format=flowed Message-ID: X-OriginalArrivalTime: 02 Nov 2004 06:59:01.0392 (UTC) FILETIME=[6EC97900:01C4C0A9] Status: RO I was studying for my ph.d qual and I came across that I couldn't solve. I was wondering if you wouldn't mind looking at it. Let {f_n} be a sequence of measurable functions defined on a measurable set E with finite measure. Suppose that a family {f_n} is pointwise bounded, that is for each x \in E, there is a constant M_x such that |f_n(x)| <= M_x for all n. Show that for all epsilon >0, there is a closed set F \subset E with m( E-F) < \epsilon such that the family is uniformly bounded on F. That is , show that there is a constant M such that |f_n(x)| <= M for all x \in F and all n. Any help you could give would be greatly appreciated. Thank you for your time Sarh Wright _________________________________________________________________ Express yourself instantly with MSN Messenger! Download today - it's FREE! XXXXXXXmessenger.msn.click-url.com/go/onm00200471ave/direct/01/