Return-Path: Delivered-To: apmail-commons-dev-archive@www.apache.org Received: (qmail 73662 invoked from network); 3 Jan 2011 05:27:02 -0000 Received: from hermes.apache.org (HELO mail.apache.org) (140.211.11.3) by minotaur.apache.org with SMTP; 3 Jan 2011 05:27:02 -0000 Received: (qmail 11897 invoked by uid 500); 3 Jan 2011 05:27:01 -0000 Delivered-To: apmail-commons-dev-archive@commons.apache.org Received: (qmail 11613 invoked by uid 500); 3 Jan 2011 05:27:01 -0000 Mailing-List: contact dev-help@commons.apache.org; run by ezmlm Precedence: bulk List-Help: List-Unsubscribe: List-Post: List-Id: Reply-To: "Commons Developers List" Delivered-To: mailing list dev@commons.apache.org Received: (qmail 11604 invoked by uid 99); 3 Jan 2011 05:27:00 -0000 Received: from athena.apache.org (HELO athena.apache.org) (140.211.11.136) by apache.org (qpsmtpd/0.29) with ESMTP; Mon, 03 Jan 2011 05:27:00 +0000 X-ASF-Spam-Status: No, hits=1.5 required=10.0 tests=FREEMAIL_FROM,HTML_MESSAGE,RCVD_IN_DNSWL_LOW,RFC_ABUSE_POST,SPF_PASS X-Spam-Check-By: apache.org Received-SPF: pass (athena.apache.org: domain of phil.steitz@gmail.com designates 209.85.214.43 as permitted sender) Received: from [209.85.214.43] (HELO mail-bw0-f43.google.com) (209.85.214.43) by apache.org (qpsmtpd/0.29) with ESMTP; Mon, 03 Jan 2011 05:26:54 +0000 Received: by bwz14 with SMTP id 14so12434436bwz.30 for ; Sun, 02 Jan 2011 21:26:33 -0800 (PST) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=gamma; h=domainkey-signature:mime-version:received:received:in-reply-to :references:date:message-id:subject:from:to:content-type; bh=whd5XoQcSaf8bQeqtQdAHtcWA3WljywpnahcNtUv67U=; b=iXtbT1DrZ8WLzaB1G84Xqhd1z8S77CfIB45g5fYAX4voGjD3zQmgUPQEKCXXUFSjtZ yl/M1dngtrM54pN+jWC5oV4iNI1qTsgar85pPqdyQOw15SqGvPScbVafbcmP0Y2NVGi+ l1E0PY4se2O5v+Nv2Tw919ZmwJiAChGa1yj+U= DomainKey-Signature: a=rsa-sha1; c=nofws; d=gmail.com; s=gamma; h=mime-version:in-reply-to:references:date:message-id:subject:from:to :content-type; b=fALvA93DtNS6q5ZFf2RNw6ySBFoMmD15bz0pOMPw7G/Whw8kuuv5+JmHb4levH9E67 rJprPUhdzNAu/wWBKGfDHXQSBoCn63s4LEcPq/fEll8DlCOo0oC+wVmJFsM029ohv5XT xY7A9nOPlwo0N7R6IFbpQxCJMOP47apldUka0= MIME-Version: 1.0 Received: by 10.204.126.138 with SMTP id c10mr15666535bks.156.1294032391859; Sun, 02 Jan 2011 21:26:31 -0800 (PST) Received: by 10.204.48.141 with HTTP; Sun, 2 Jan 2011 21:26:31 -0800 (PST) In-Reply-To: References: Date: Mon, 3 Jan 2011 00:26:31 -0500 Message-ID: Subject: Re: [math] meaning of "support" in distributions classes From: Phil Steitz To: Commons Developers List Content-Type: multipart/alternative; boundary=0016e6d976520b6c8a0498ea6568 --0016e6d976520b6c8a0498ea6568 Content-Type: text/plain; charset=ISO-8859-1 On Sun, Jan 2, 2011 at 11:46 PM, Ted Dunning wrote: > On Sun, Jan 2, 2011 at 2:05 PM, Phil Steitz wrote: > > > We don't precisely define what we mean by the support of a distribution > > anywhere. I have been assuming that we mean the smallest closed set such > > that its complement has probability 0. > > > Why closed? > > Why not just the smallest set such that the complement has probability 0? > Because that in general will not be well-defined. Consider, for example, the support of the Beta distribution. The smallest closed set whose complement has probability 0 is [0, 1] (independently of the parameters). If the definition does not require that the set be closed, then when you consider (0, 1], [0, 1), [0, 1] - {x} for any x in [0,1], or [0, 1] minus any finite number of points...you see that there will be no unique smallest (in terms of inclusion) set whose complement has probability 0. Phil --0016e6d976520b6c8a0498ea6568--