Summary: Real Analysis, course outline
Denis Labutin
1 Measure theory I
1. Sigma algebras. Let A be a collection of subsets of some fixed set .
It is called a -algebra with the unit element if
(a) , A ;
(b) E A = c
E A ;
(c) Ej A , j = 1, 2, . . . =
j
Ej A .
Prove that a -algebra A is closed under countable number of the set
theoretic operations ( , , \ , (·)c
).
2. For a sequence of sets Ej define
lim sup
j
Ej = {points which belong to infinitely many Ej},
lim inf
j

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

Collections: Mathematics