The simplest LLN -- Law of Large Numbers -- is that the observed frequency of an event [post-experimental concept] converges to the theoretical probability of the event [pre-experimental concept] -- this may be called the MICRO-LLN.
A small extension of this shows that histogram of random samples from data converge to the histogram of the data. This is what I call the mini-LLN. The First Preliminary Lecture for Bayesian Econometrics covers the mini-LLN:
BE Pre-L01: Convergence of Frequencies to Probabilities [You Tube Video Lecture 1 Hour]
The FULL LLN shows that sample moments of random variables converge to corresponding theoretical expected values. This will be covered in later lectures.
This first lecture deals with the concept of histograms. How to make and interpret histograms for data sets is discussed in detail.
This material is closely parallel equivalent to the material covered in Lecture 07 of Introduction to Statistics -- Please follow the link for ALL relevant course materials, including links to videos, lab exercises, quizzes, lecture notes etc.
L07: Histograms (intro stats) - Background material on how to make and interpret histograms
L07: Histograms - Viewable Video Lecture on Histograms
Convergence of Frequencies to Probabilities - Video Lecture on material covered in Chap 08: Matching Samples to Populations