Measles can remain in the air and on surfaces for quite a long time. I seem to recall it's roughly 2 1/2 hours of existing outside of the body before the virus is inactive. Its persistence in public places is why this is a particularly rapidly-spreading disease among the unvaccinated and under-vaccinated.
If you didn't suffer through the hell of this murderous infection as a child, please make damn sure you and your children are current with your vaccinations. There is a simple test to determine if you need a booster.
"When I was a child, I had a fever
My hands felt just like two balloons" - Pink Floyd
Every parent exposing their children to the measles commits an act of child abuse.