Apparently super is slightly more future proof than using the specific base class name (i.e. RequestHandler) as it allows mixins, etc.
class MyHandler( webapp2.RequestHandler ):
def __init__( self, request, response ):
self.myService = MyService()
super( MyHandler, self ).__init__( request, response ) # inherits from RequestHandler
Alternatively , this seems to work though my IDE complains https://github.com/pizzapanther/Python-Google-Drive-Presentation/blob/master/google_appengine/lib/webapp2/docs/guide/handlers.rst
class MyHandler( webapp2.RequestHandler ):
def __init__( self, request, response ):
self.initialize( request, response )
# custom stuff
self.myService = MyService()