If you remember last month I wrote about DBCC CHECKDB and Azure SQL Database, more specifically whose responsibility (Microsoft’s) it is and ponderings on how it is actually done. (https://blobeater.blog/2017/09/04/dbcc-checkdb-azure-sql-database/)
Recall that is consumes a lot of DTUs running CHECKDB on your Azure SQL Database so I had doubts that it is something we as users should be doing, well I am happy to say there is now official documentation on this subject.
I did a quick overview chart on techniques used and all of them make sense.
You can find the article here: https://azure.microsoft.com/en-us/blog/data-integrity-in-azure-sql-database/
Please see the link for more details especially how they would deal with YOUR DATA if integrity is comprised i.e. corruption. It is quite thorough. I particularly like the lost write protection where it tracks page writes and their associated LSNs (Log Sequence Numbers).