Are dogs allowed in LAX airport terminals?

I keep my little guy in a carrier, but some irresponsible caregivers walk their dogs on a leash. I don't know what diseases they carry or what their temperament is. Isn't there a law to keep them in a carrier? It's just like walking your dog in a courthouse or other government building. Please help!

If the dog is there to be shipped on a flight, it only needs to be leashed. It's a little hard to drag a 70 lb dog in a carrier around...