Which law in probability theory states the following?
If we have a large enough number of samples, their histogram function converges their true probability density function. (for a continuous random variable)
I know that "In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed."
But this law is just about expected value. It does not include variance or probability density function.