Chapter 4 definitions

σ-algebra on X & (X, A) a measurable space

σ(C)

Borel σ-algebra of (M, d)

Measurable function

If f −1 (A) is measurable for every open set A, then ____ ?

simple function

Let f : X → R be a non-negative measurable function. Then there is a non-negative increasing sequence of simple functions _____

µ a measure and (X, A, µ)

(X, µ) a measure space

f is integrable

integral of a simple function

Let f and g be integrable functions, with f(x) ≤ g(x) for all x ∈ X. Then ___