My Blog
My Blog
I am still working on probability theory.
I am still working on Chapter 14 and have corrected a couple of mistakes. The Law of Large Numbers was not proved corrected. The earlier proof only yields the Weak Law of Large Numbers. Now, I have added the Strong Law of Large Numbers at the end of Section 14.4. The proof for the Central Limit Theorem was not entirely correct. The proof is now done correctly and had to involve the logarithm function on the complex plane. The result has to be done properly via a trip to the theory of manifold. I have add Section 12.10 on manifolds. My treatment of manifold is slightly different from the usual exposure of manifold. I think that my treatment is more general. It allows me to resolve the logarithm function and prove the Jacobi identity for vector fields. The proof of the Central Limit Theorem has been corrected accordingly, which I haven’t fully reviewed yet. I am working on the Chapter 14 for a complete review and hopefully finish the book by the end of this year.
Wednesday, August 28, 2019