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
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 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
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 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