5. Lebesgue Integration - Probability
Tutorial 5: Lebesgue Integration 3 Definition 41 Let (Ω,F) be a measurable space, and s be a simple function on (Ω,F).Wecallpartition of the simple function s,any representation of the form: s = n i=1 αi1Ai where n ≥ 1, αi ∈ R+, Ai ∈Fand Ω=A1...An. Exercise 4. Lets bea simplefunction on (Ω,F) with twopartitions: s = n i=1 αi1Ai = m j=1 βj1Bj 1. Show that s = i,j αi1Ai∩Bj is a ...
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