A much easier answered question, "What doesn't run on battery?"
Answer, "the microwave and air conditioner", unless you are a solar powered "big Strap" then there is nothing that does not run on battery thru a 3000 watt inverter.
If its the television you are concerned about, just get a little cheap 150 watt "inverter" connect it to the batteries, and plug in the ty/dvd/sat receiver.
And if it mite be "sat tv" you want, just take your sat receiver from home, and connect it to a portable tripod dish,......or install an automatic sat finder dish on the RV,.....or buy a portable automatic sat finder dish.
This is all very simple and expensive ??;)