If m: message, M: message space, k: key, K: keyspace, c: cipher, C: cipher space and $E_k$: encryption function, such that $E_k(m) = c,\ m,m^* \in M,\ k\in K,\ c\in C.$
Then, what do the following notations actually mean in plain English?
What does it mean by $C=c$? If it means "If $C$ takes the value of $c$", to my understanding it is meaningless. Why would $C$ take the value of $c$? $c$ is a part of the whole message $C$. The same is true for $M$ and $m$.