Must I do your research for you? If I did, would you even be open-minded? Let's find out.

First, you cannot get just a measles vaccine, you can only get an MMR vaccine, which is owned solely by Merck. Did you know that? [ http://www.askdrsears.com/topics/health-concerns/vaccines/separate-measles-mumps-rubella-vaccines-longer-available-can-parents ]

Second, let's go into the other parts of the MMR vaccine.. let's start with mumps and the revelation of two whistleblowers from inside Merck taken from this Forbes article:

Anyone who falls on either side of the debate about vaccines’ alleged potential to cause harm is sure to have heard the big news this week — the unsealing of a whistleblower suit against Merck, filed back in 2010 by two former employees accusing the drugmaker of overstating the effectiveness of its mumps, measles, and rubella vaccine.

The scientists claim Merck defrauded the U.S. government by causing it to purchase an estimated four million doses of mislabeled and misbranded MMR vaccine per year for at least a decade, and helped ignite two recent mumps outbreaks that the allegedly ineffective vaccine was intended to prevent in the first place .

“ As the single largest purchaser of childhood vaccines (accounting for more than 50 percent of all vaccine purchasers), the United States is by far the largest financial victim of Merck’s fraud. But the ultimate victims here are the millions of children who every year are being injected with a mumps vaccine that is not providing them with an adequate level of protection against mumps. And while this is a disease the CDC targeted to eradicate by now, the failure in Merck’s vaccine has allowed this disease to linger with significant outbreaks continuing to occur ,” the suit alleges.
[ http://www.forbes.com/sites/gerganakoleva/2012/06/27/merck-whistleblower-suit-a-boon-to-anti-vaccination-advocates-though-it-stresses-importance-of-vaccines/ ]

It refers to a 2006 mumps outbreak in the Midwest, in which 6,500 cases were reported among a highly vaccinated population, and another in 2009, in which 5,000 cases were confirmed. By comparison, the annual average of mumps cases in the U.S. in the two decades preceding the 2006 outbreak was 265; before the introduction of the single-shot Mumpsvax vaccine in 1967, there were approximately 200,000 cases of the disease, according to the 55-page document.

I will continue this later (because it's fucking Sunday and I have a life) but:

Beyond the above stated, it is known that

"Mortality due to tuberculosis, diphtheria, scarlet fever, whooping cough, measles, typhoid, puerperal fever and infant gastro-enteritis **started to fall long before the introduction of immunization and/or antibiotics." [Guberan, E. "Tendances de la mortalite en Suisse" Schweiz, Med Wschr. 110, 1980. p. 574]