Great question. Maybe speak with a local builder to see what reinforcement may be necessary if any?

If you are using 2cm granite (3/4") this weighs 12lbs/ft2 if your using 3cm (1-1/4") granite it weighs 18lbs /ft2. If you are able to add braces between the joists it would be a good idea. If you are uisng the 3/4' you shouldn't have a problem with the weight as it is distributed across the span.
If the weight is a concern, go with the 3/4" stone with a build up edge detail. Also would suggest you lay the stone on a plywood counter is its the 3/4", if its the 1-1/4" no need for the plywood.
Hope this helps you abit.