I sent the final list to Professor Lehmann and he was very grateful, writing several letters in response. I would also like to encourage you to keep your eyes open for any more errors. For example, no awkward word choices or questionable commas. I use TeX notation to denote mathematical symbols. The first sentence of the hint is false.
Nothing is harmed by deleting it.
The statement is not true. This happens 3 times. The statement is false. The absolute value of the sample mean tends to infinity in this case, but with probability 1, the sample mean itself does not converge to any value, finite or infinite. Also, a right bracket is missing after the hint.