Sample Space

The Set of all possible outcomes of an Experiment, usually denoted $S$ or $\Omega$. It is the Universe for Probability Theory where every Event $A$ satisfies $A\subseteq S$ (see Correspondance to Set Theory).

Finite Sample Space

A Sample Space where $|S|<\infty$

Means we can use Cardinality and Combinatorics with $P(A)=\frac{|A|}{|S|}$ to get Probability

Simple Sample Space

A Finite Sample Space where all singleton outcomes are equiprobable: $P(\{\omega \})=1/|S|$ for every $\omega \in S$, so $P(A)=|A|/|S|$ for any Event $A\subseteq S$