... Prove that the collection D in the proof of Theorem 2.1 is a σ-algebra.2. Prove Theorem 2.3.3. Prove Theorem 2.4 for the max, sup, limsup and lim cases.4. Complete the proof of Theorem 2.5, ... eventcorresponds to the set Ak,n of elements ω of Ω for which the sum of the first n elements in the string involved is equal to k. For example, the set A1,2 consists of all ω of the type (1,0, ) and (0,1, ... identical. The proof of this theorem is complicated, and is therefore given in Appendix 2.A at the end of this chapter. The same applies to the following useful result, which is known as the inversionformula...