Research proof index

For every bounded, finitely supported function $f$, almost every point $x$ admits a sequence of balls $B(c_i,r_i)$ that all contain $x$, whose radii tend to $0$ from above, and whose averages converge to $f(x)$:

$\dashint_{B(c_i,r_i)} f(y)\,dy\longrightarrow f(x).$