Since mmap objects are said to "behave like both bytearray and like file objects" I believe it's appropriate for the mmap.write() method to return the number of bytes written like write() of other file objects/interfaces I could find in the standard library for consistency reasons:

https://docs.python.org/3/library/io.html#io.BufferedIOBase.write
https://docs.python.org/3/library/io.html#io.BufferedWriter.write
https://docs.python.org/3/library/io.html#io.RawIOBase.write
https://docs.python.org/3/library/io.html#io.TextIOBase.write

Why I believe this would be useful: code that writes to file objects and tests the number of bytes/characters written right now will likely fail when it's passed a mmap object because its write() method returns None. With this patch applied it'll work transparently.

Please find proposed patch attached, I included information about the exception type in the documentation as it seems fitting (apologies for generating the patch using Git, I'll generate using Mercurial if necessary).