Consider the functions f,g:[0,1]toR defined by f(x)=1 if x is rational, 0 if x is irrational; and g(x)=1/x if 0<xle1, g(0)=0. Then:

(D) f is Lebesgue integrable and g is not Lebesgue integrable

Q24Section II (Mathematics)24 of 145

Dirichlet's function is Lebesgue- but not Riemann-integrable; $1/x$ is neither

Consider the functions $f,g:[0,1]\to\mathbb{R}$ defined by $f(x)=1$ if $x$ is rational, $0$ if $x$ is irrational; and $g(x)=1/x$ if $0<x\le1$ , $g(0)=0$ . Then:

Pick an option to check your answer.

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