Such a livestreamer would have to use data connections with fallbacks from multiple mobile data providers and possible a satellite fallback, and a mobile signal booster to bring inside venues.
Last I checked that was stupid expensive. Here in the Bay Area Caltrain doesn't have wifi (lol?) so I went on a kick of "I'm gonna get THE BEST MOBILE INTERNET AVAILABLE ANYWHERE" to use on the train. I ended up with a simple Verizon jetpack because the satellite internet stuff comes in briefcases, is CRAZY expensive (like thousands of dollars for the equipment and hundreds for the service) and on top of all that it's stupid slow.
$2,239, up to 492Kbps: http://www.groundcontrol.com/BGAN.htm