Definition of unique measure

Question

In the Notes on Stochastic Finance by Nicolas Privault, we can find that

when the risk-neutral probability measure is unique, the market is said to be complete.

To say that a measure is unique we must have a notion of equivalent measures.

Let $(\Omega,\Sigma)$ - measurable space. Let $a,b$ - measures.

In the context above, which equivalence notion is used?

1. Measure $a$ is equivalent to $b$ when $$\forall_{S\in\Sigma}\;a(S)=b(S)$$

or

2. Measure $a$ is equivalent to $b$ when $$a\ll b \land b\ll a$$ where $\ll$ denotes the absolute continuity of measures.