This is a problem from Harmonic Analysis, I was reading about Fourier Transform, more likely about Singular Integrals. Can anyone help me to prove this problem?
$f_r(x)= \frac{1}{|B(a, r)|}\chi B(a, r) (x)$
forms an approximate identity as $r\rightarrow 0. $
This term was used in Lebesgue's differentiation theorem's proof. Also no idea bout the term $\chi$.
in my opinion
$f_r(x)= \frac{1}{|B(x, r)|} \int_{B(x, r)}f(y)dy$
thank you