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Duplicate Content - Get it right or perish [webmasterworld.com]
However, tedster is correct that unless the content at the non-www form is different than that at the www form you are looking at some form of a Google wash (duplicate content issue/problem/whatever).
You really need to be careful.
[edited by: theBear at 4:27 pm (utc) on Sep. 21, 2006]
If you want your site to work if visitor writes either "www.sample.com" or "sample.com" in browers, you should choose one of these versions as canonical, as set up 301 redirect from other versions to this one. The same, if you own multiple domains for one site, for example, with different spellings of company name, you should 301 redirect all of them to the proper version, if you want to be in accordance with Google guidelines.
If there is a proper 301 redirect from non-www to www version, or the other way round, and some backlinks to both versions, Google responds properly to both version without duplicate content issues. Also setting the preferred URL version in Google webmaster tools can help. But don't ever allow Google to index both URL versions without telling it which one is canonical!
I say "might" because pre-existing links could do you no good if they are off-topic for your new content. I think you need to research things a bit.