Editing Cheap talk (section)

====Messages====
While messages could ex-ante assume an infinite number of possible values ''μ(t)'' for the infinite number of possible states of the world ''t'', actually they may take only a finite number of values ''(m<sub>1</sub>, m<sub>2</sub>, . . . , m<sub>N</sub>)''.

Thus an equilibrium may be characterized by a partition ''(t<sub>0</sub>(N), t<sub>1</sub>(N). . . t<sub>N</sub>(N))'' of the set of types [0, 1],
where ''0 = t<sub>0</sub>(N) < t<sub>1</sub>(N) < . . . < t<sub>N</sub>(N) = 1''. This partition is shown on the top right segment of Figure 1.

The ''t<sub>i</sub>(N)''{{'}}s are the bounds of intervals where the messages are constant: for ''t<sub>i-1</sub>(N) < t < t<sub>i</sub>(N), μ(t) = m<sub>i</sub>''.