Prove Theorem 25.3 for d = 1, where each partition consists of nonaccumulating intervals, without the condition that the sequence of partitions is nested. Hint: Compare Problem 24.6.  Prove Lemma...

Prove Theorem 25.3 for d = 1, where each partition consists of nonaccumulating intervals, without the condition that the sequence of partitions is nested. Hint: Compare Problem 24.6.

 Prove Lemma 25.4. Hint: Use the truncation YL = Y IY ≤L + LIY >L for Y ≥ 0 and notice for mL(x) = E{YL|X = x} that for > 0 an integer L0(x) exists with

                                     |mL(x) − m(x)|

 for all L>L0(x) and for µ-almost all x.