: Complex Variables and Integral Transforms (3 credits)
MAT 136

Summer 2014
Math 136 / Stat 219  Stochastic Processes
Homework Set 2, Autumn 2011, Due: October 12
1. Exercise 1.3.21.
ANS: (i) The triangle inequality for the Lq norm is X + Y q Xq + Y q (X, Y Lq ). So
q.m.
Xn q Xq  Xn Xq , and since Xn X implies Xn Xq 0, it can
: Complex Variables and Integral Transforms (3 credits)
MAT 136

Summer 2014
Math 136/Stat 219 Homework 3
October 18, 2011
1. Exercise 2.2.13 To show that the inmum d = infcfw_ h g : g G is actually
achieved by some g G, we will demonstrate a Cauchy sequence gn with the
property that h gn converges to d. Recall the parallelogram l
: Complex Variables and Integral Transforms (3 credits)
MAT 136

Summer 2014
Math 136/Stat 219 Homework 1
Yunjiang Jiang
October 5, 2011
Question 0.1.
1. For F = (cfw_[0, 1/2], (1/2, 1]), the elements of the sigma eld are
, [0, 1/2], (1/2, 1], [0, 1]. So, any Fmeasurable function must be separately constant on the indivisible ele