Understanding the Fat Cantor Set & Proving Its Measure

[math8]

What is the definition of a fat cantor set? How do I show that the fat cantor set has positive Lebesgue measure and does not contain any interval.

I know for the cantor set that at each stage, we remove the middle third of each interval starting with [0,1]. I am wondering if instead for the fat Cantor set, there is maybe a sequence of positive numbers {cn} and at the stage n, we need to remove the middle cnth of each interval but in this case, should the cn be odd?
I know how to prove that the cantor set has measure 0 and that it contains no interval, but I am not sure how to proceed for the fat cantor set.

 

[HallsofIvy]

Check this:
http://en.wikipedia.org/wiki/Smith-Volterra-Cantor_set

Essentially, you form the "fat" Cantor set by removing less than 1/3 of the interval each, say 1/4 instead of 1/3, thus leaving a "fatter" set.

 

[math8]

Thanks, that is very helpful.