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Here is the classic Dirichlet function:

Let, for x ∈ [0, 1],

f (x) =1 /q if x = p /q, p,q in Z

or 0 if x is irrational.

Show that f (x) is Riemann integrable and give the value of the integral.

Is this actually true?

Let, for x ∈ [0, 1],

f (x) =1 /q if x = p /q, p,q in Z

or 0 if x is irrational.

Show that f (x) is Riemann integrable and give the value of the integral.

Is this actually true?

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