Chapter 7 - Product Measures Flashcards
1
Q
Define the family of all finite unions of rectangles.
State Lemma 7.1 on families of finite unions of rectangles and algebras.
A
2
Q
Define the product sigma-algebra of E and F.
State the result on the product sigma-algebra of Borel sigma-algebras.
A
3
Q
Define a sigma-finite measure space.
State THM 7.2 - The Product Measure Theorem.
State the result on the product of Lebesgue measures.
A
4
Q
Define the x and y-sections of A and f.
State Lemma 7.3 on these sections.
A
5
Q
Define a monotone class.
State the monotone class lemma.
A
6
Q
State Lemma 7.5 on measuring A using two functions f and g.
A
7
Q
State Tonelli’s Theorem.
State Fubini’s Theorem.
A
