Let $(\Omega, B, \mu)$ be a measure space. How can we characterize the space $(\Omega, B, \mu)$ so that
- the counting measure on $B$ is absolutely continuous with respect to $\mu$?
- the Dirac measure on $B$ is absolutely continuous with respect to $\mu$?
Edit: What I mean by the Dirac measure on $B$ is the following: Let $x\in \Omega$. Then the Dirac measure at $x$ assigns $1$ to a set in $B$ that contains $x$ and $0$ to a set that does not contain $x$.