Chapter 1 Sigma-Algebras
1.1 Denition
Consider a set X . A algebra F of subsets of X is a collection F of subsets of X satisfying the following conditions: (a) F (b) if B F then its complement B c is also in F (c) if B1 , B2 , . is a countable collection
Chapter 2 Topological Spaces
This chapter contains a very bare summary of some basic facts from topology.
2.1
Denition of Topology
A topology O on a set X is a collection of subsets of X satisfying the following conditions: (T1) O (T2) X O (T3) O is close
Chapter 12 The Hahn-Banach Theorem
In this chapter V is a real or complex vector space. The scalars will be taken to be real until the very last result, the comlex-version of the Hahn-Banach theorem.
12.1
The geometric setting
x + A = cfw_x + a : a A
If A
Lecture 2. Measure and Integration There are several ways of presenting the denition of integration with respect to a measure. We will follow, more or less, the approach of Rudins Real and Complex Analysis - this is probably the fastest route. Conventions
Chapter 5 Topological Vector Spaces
In this chapter V is a real or complex vector space.
5.1
Topological Vector Spaces
A complex vector space V equipped with a topology is a broad-sense topological vector space if the mappings V V V : (x, y ) x + y C V V
Questions of Policy
Questions of policy concern what should be done, what procedures should be adopted, what law should
be changed, in short, what policy should be followed. In some speeches you may want to defend a specific
policy whereas in other speech