Question: fX (u) du for a, b R with a b. (5.29) Proof We argue as follows: P(X = x) = lim 0 P(x

fX (u) du for

a, b ∈ R with a ≤

b. (5.29)

Proof We argue as follows:

P(X = x) = lim

ǫ↓0 P(x − ǫ < X ≤ x)

= lim

ǫ↓0



FX (x) − FX (x − ǫ)



by (5.10)

= lim

ǫ↓0 Z x x−ǫ

fX (u) du by (5.21)

= 0.

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