I have seen that pages inside gmail carry page rank. Does this imply that this page rank is fake? If it is genuine can it somehow be used to add to other site's PR?

I'm really confused by your question. Pagerank is simply a very unreliable / "fake" / old data representation of how many other sites and webpages link to a particular page.

I think what ncaditya was referring to was the fact that when on gmail, the toolbar shows a page rank. Mine says it is about a 2.

However looking at the source code of the page, the email is all pulled in through external functions. So I doubt highly that PR would pass through. Plus even if it did, I would imagine they would use the No follow tag to prevent any PR leakage.

Hope that helps!

Oh I put no value in toolbar PR no matter what.

It's just the toolbar guessing. You see it happen on forum search pages all the time. I've seen forum search pages that were just created have a PR of 9. Those pages have no PR so I wouldn't worry about trying to capitalize on it.