You can read an abstract of the study here.
In a Reuters article on the findings, researcher Paul Thompson of UCLA said the following:
"In all the maelstrom of activities you do, exercise and a low-fat diet are genuinely saving your brain from both stroke and Alzheimer's."
According to the article, Thompson's team compared MRI images taken of the brains of 206 healthy people between age 55 and 90 at 58 centers taking part in a five-year Alzheimer's Disease Neuroimaging Initiative. Their goal is to find ways for people to resist the mind-robbing disease.
A key takeaway is for all of us to maintain a healthy lifestyle that includes eating healthful meals in moderate portions and daily exercising.