To my (maybe wrong) understanding, the central limit theorem states that, whatever the probabilistic function that we choose, if we add the sum of a random variable that is following a given fixed chosen probabilistic function, it will eventually follow a gaussian distribution.
https://en.wikipedia.org/wiki/Central_limit_theorem
If on purpose, I choose a Dirac at x value=1, as probabilistic function (probability of 1 only for a single value), do I understand that the sum of the random variable will never follow a gaussian but will follow a Dirac distribution at a x value=number of experiments ?
Where on the definition of the Central limit theorem my counter-example is "prevented" ?
The Dirac distribution is just a normal distribution whose variance is zero, so in this case the CLT still holds (rather trivially, since the sample average and all the r.v.'s are constant with probability $1$).