3.2 Example. Consider the Dirichlet function f: [0, 1] → R defined by if x is rational f(x)= if x is irrational. The function f is clearly bounded and measurable on [0, 1] and hence Lebesgue integrable. Also f(x)=0. However, ƒ is not Riemann inte- 0

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Q: Show also that the function ln(z) is unique up to addition of a constant 2πik, k ∈ Z.

A: ln(mn) =ln(m) +ln(n)  ln(am) =mln(a)

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