  We express continuous $\times p,\times q$-invariant measures on the unit
circle via some simple forms. On one hand, a continuous $\times p,\times
q$-invariant measure is the weak-$*$ limit of average of Dirac measures along
an irrational orbit. On the other hand, a continuous $\times p,\times
q$-invariant measure is a continuous function on $[0,1]$ satisfying certain
function equations.
