Greater than 99% of people who receive two doses (with the first dose administered on or after 12 months of age) of MMR vaccine, per U.S. Centers for Disease Control and Prevention (CDC) recommendations, develop immunity to measles.
While it is possible to contract measles after two doses of the vaccine, it is very uncommon. As with many other viral vaccines, those who contract the virus while vaccinated seem to have more mild symptoms and are less likely to spread the virus to others.