Is it possible to change web app scripts domain to custom domain name

[NARONGKORN KITRUNGROT]

Is it possible to change the web app scripts domain to a custom domain name, I want to change from the default domain into a short one, 

Can I add Google AdSense to web app scripts? I have try insert default URL which I got from deploy (anyone) but I got "The URL has a restricted domain.".

[Iain Bailey]

This isn't possible with GAS as far as I know.

The best workaround I've found is to use Tinyurl to redirect to the web app. Unsure if AdSense can be used with this though.