Lebesgue Differentiation Theorem — Doubling Spaces

Lebesgue Differentiation Theorem claims that for integrable functions, at almost every point x the integral average of the function over the ball of radius r centered at x converges to f(x) as r goes to zero. See the elegant proof of this result as a corollary of the Hardy-Littlewood maximal function in arbitrary metric measure space with a doubling measure.

[luisguamushig]

help me please, i want to know covering lemma on doubling metric space, i can find in the metric space, but i cant find in the doubling metric space, can you help me ? pleaaaase
im mathematic