Welcome to WebmasterWorld Guest from 18.104.22.168
Once you specify your preference here, it may take some time for changes to be reflected in our index. While Google doesn't guarantee that we'll show your URLs in the form that you prefer, we will use your choice as a suggestion to improve our indexing.
If you want to be 100% certain, you should install a 301 redirect from the "no-www" form to the "with-www" form of your urls.
The details on how to do that will be specific to the server you are using. There's a good thread covering many of these issues in the Hot Topics area [webmasterworld.com], which is always pinned to the top of this forum's index page:
Why Does Google Treat "www" & "no-www" As Different? [webmasterworld.com]