Define
$$A \hat + B = {a + b \mid a \in A, b \in B, a \ne b}$$
For $A$ an interval in $\mathbb Z$, $|A \hat + A| = 2|A| - 3$. The Erdős-Heilbronn conjecture says this is best possible.
Let $A, B$ be sets in $\mathbb F_p$ such that $1 \le |A| < |B|$ and $|A| + |B| \le p + 2$. Then
$$|A \hat + B| \ge |A| + |B| - 2$$
This is Theorem 2.7 in the lecture notes.
Define
$$A \hat + B = {a + b \mid a \in A, b \in B, a \ne b}$$
For$A$ an interval in $\mathbb Z$ , $|A \hat + A| = 2|A| - 3$ . The Erdős-Heilbronn conjecture says this is best possible.
Let$A, B$ be sets in $\mathbb F_p$ such that $1 \le |A| < |B|$ and $|A| + |B| \le p + 2$ . Then
$$|A \hat + B| \ge |A| + |B| - 2$$
This is Theorem 2.7 in the lecture notes.