  We give some new results on algebraic independence within Mahler's method,
including algebraic independence of values at transcendental points. We also
give some new measures of algebraic independence for infinite series of
numbers. In particular, our results furnishes, for $n\geq 1$ arbitrarily large,
new examples of sets $(\theta_1,...,\theta_n)\in\mrr^n$ normal in the sense of
definition formulated by Grigory Chudnovsky (1980).
