A much simpler way of thinking about it is:
What is the chance that if I pick an infinite number of random natural numbers between 0 and 9 that all of them are 0?
You're missing the repeating fractions but it gets the flavor of what's actually happening across much better than a Lebesgue integral.
https://www.americanscientist.org/sites/americanscientist.or...
(I kid, I kid)
A much simpler way of thinking about it is:
What is the chance that if I pick an infinite number of random natural numbers between 0 and 9 that all of them are 0?
You're missing the repeating fractions but it gets the flavor of what's actually happening across much better than a Lebesgue integral.