In John Watrous's The Theory of Quantum Information the author introduces Markov's inequality as follows:
The first theorem to be stated in this subsection is Markov’s inequality, which provides a sometimes coarse upper bound on the probability that a nonnegative random variable exceeds a given threshold value.
Also, in this section the author clarifies that
the theorem statements that follow should be understood to apply to random variables distributed with respect to Borel probability measures.
The inequality itself as stated as follows:
Theorem 1.13 (Markov’s inequality) Let X be a random variable taking nonnegative real values, and let ε > 0 be a positive real number. It holds that
$${\text{Pr}(X\geq\epsilon) \leq \frac{E(X)}{\epsilon}}.$$
Where previously the following notational convention was established:
${\text{Pr}(X\geq\epsilon) \iff}$''${\mu(\{u\in\mathcal{A}:X(u)\in\mathcal{B}\})}$ for ${\mathcal{B}=\{\alpha\in\mathbb{R}:\alpha\geq\epsilon\}}$'' where $\mathcal{B}$ is a Borel subset of $\mathbb{R}$, ${\mathcal{A}}$ is a subset of some real or complex vector space ${\mathcal{V}}$, ${\text{Borel}(\mathcal{A})}$ is the collection of Borel subsets of ${\mathcal{A}}$, and ${\mu: Borel(\mathcal{A}) \to [0, 1]}$ is a Borel probability measure.
I do not understand what "sometimes coarse" refers to in this context.