Since you're interested in machine learning, I'd skip probability and mesaure, and jump right into the ML. Andrew Ng's course is a great place to start. You can literally finish it in two weeks.
Play with what you've learned for a few weeks, then go back to the roots and study some probabilities. If you're an engineer, then I'm puzzled with how you managed to skip in in college. It used to be the required course in engineering. Anyhow, you can catch up by taking MIT OCW course here.
I don't think you need measure theory. Nobody needs measure theory. Those who do, they won't come here to ask, because their advisor will tell them which course to take. If you don't have an advisor then you definitely don't need it. Tautology, but true.
The thing with a measure theory's that you can't learn it by "easy reading". You have to do the exercises and problems, basically, do it hard way. That's virtually impossible outside of the class room, in my opinion. The best option here is to take a class at the local college, if they offer such. Sometimes, PhD level probabilities course will do the measure and probabilities in one class, which is probably the best deal. I would not recommend taking a pure measure theory class in Math department, unless you really want to torture yourself, though in the end you'd be greatly satisfied.