I have read – but can't find the link (and as usual Civipedia sucks) – that Entertainment districts can be shared between cities up to 6 tiles away.
I found the districts 'cheat sheet' on a number of sites but it doesn't mention this.
Is this true – and can any other districts be shared between multiple cities?
If so at what tile distance – and is there a city limit within that distance? Are all benefits shared or only some buildings?
How can you check which districts are affecting which cities?
Best Answer
AFAIK, only the entertainment and industrial districts share bonuses to nearby cities (along with the Colosseum wonder) and only the buildings who specify shared bonuses will do so.
Tile distance - Do the ranged effects of districts or the Colosseum depend on the actual district location or on the city center?
Benefits shared - Do "Bonus extending" building (Factory, Zoo, ...) stack? (No city limit I believe, or it is more than 4 at least.)
Finally this is covered a bit in the other posts, but by hovering over the production of a particular city, you can see how much production it receives from particular buildings. No way to tell which city provides the bonuses, but it's easy enough to figure out which districts are within 6 tiles.