Here's the documentation overview for In App Billing, where it says:
Google Play tracks and manages the ownership information of managed products. When a user purchases a managed product, Google Play stores the purchase information for each product on a per-user basis. This enables you to later query Google Play at any time to restore the state of the products a specific user has purchased. This information is persistent on the Google Play servers even if the user uninstalls the application or if they change devices.
To provide premium content, you'll need to create a managed product that doesn't get consumed in the app when the user purchases it. In order to query the user's in-app purchases, send a getPurchases() request, that will return all the current un-consumed products owned by the user.
If you find the premium content in this response, you know the user has purchased it and can grant them the premium interface.