Editing Bernoulli process (section)

===Borel algebra===
Consider the [[countably infinite]] [[direct product]] of copies of <math>2=\{H,T\}</math>.  It is common to examine either the one-sided set <math>\Omega=2^\mathbb{N}=\{H,T\}^\mathbb{N}</math> or the two-sided set <math>\Omega=2^\mathbb{Z}</math>. There is a natural [[topology]] on this space, called the [[product topology]]. The sets in this topology are finite sequences of coin flips, that is, finite-length [[string (computer science)|strings]] of ''H'' and ''T'' (''H'' stands for heads and ''T'' stands for tails), with the rest of (infinitely long) sequence taken as "don't care".  These sets of finite sequences are referred to as [[cylinder set]]s in the product topology.  The set of all such strings forms a [[sigma algebra]], specifically, a [[Borel algebra]].  This algebra is then commonly written as <math>(\Omega, \mathcal{B})</math> where the elements of <math>\mathcal{B}</math> are the finite-length sequences of coin flips (the cylinder sets).