It's hard to tell from the image, but the I think we're looking at two different fonts here.
The "Inbox" and "COMPOSE" (and following menu items) text looks a lot like Montserrat:
If you look closely at the letter
O in "COMPOSE", it appears to be slightly narrower than the visual roundness of the
o in "Inbox". Again, it's hard to tell exactly from the image, but in my recreated example above, I dropped the Horizontal Scale down to 95% and it's pretty close.
Notice the difference of the uppercase
G at the end of "SHOPPING" compared to the same letter in "Gregory Green" in the name list. This is indeed a different font from the menu and title text. The typeface in the name list is pretty close to Source Sans Pro (slightly modified with the tracking set to -50):
Just to reiterate once more, the image posted presents very small text, which makes it difficult to determine the exact typefaces with precise accuracy. These are my best guesses based on the evidence and on current UI design typography trends.