The statement of the Calderon-Zygmund decomposition as given in Duoandikoetxea's book is the following.
For $f$ integrable on $\mathbb{R}^n$ and non-negative and given $\lambda>0$, there exist a sequence $\{Q_j\}$ of disjoint dyadic cubes such that
- $f(x) \leq \lambda$ for almost every $x \notin \cup Q_j$
- $|\cup Q_j|\leq \frac{\lVert f \rVert_1}{\lambda}$
- For each $j$, $\lambda < \frac{1}{|Q_j|} \int_{Q_j} fdx<2^n\lambda$.
In the proof, you need to consider the case when no such cubes exist. In Grafakos's proof of the theorem, he makes a note of the fact that in some cases the set $\cup Q_j$ is empty. In this case, I do not see how the the third requirement is true. If you have the empty sequence is this vacuously true? If you have the empty sequence then $\frac{1}{|Q_j|} \to \infty$ so how can 3 be true?