I have an 8830 with Verizon. Everytime I send an e-mail from gmail, i recive a copy of the e-mail in my gmail inbox on my BB. I also have a yahoo acount on my BB, and I do not have this issue.
you can also download the gmail app from your phones browser @ google.com and have the gmail app notify you via the message icon when you get a new email.
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my bb gives me
VZW 8330 4.5.0.160