  In this paper we mainly study the dynamical complexity of Birkhoff ergodic
average under the simultaneous observation of any number of continuous
functions. These results can be as generalizations of [6,35] etc. to study
Birkhorff ergodic average from one (or finite) observable function to any
number of observable functions from the dimensional perspective.
  For any topological dynamical system with $g-$almost product property and
uniform separation property, we show that any {\it jointly-irregular set}(i.e.,
the intersection of a series of $\phi-$irregular sets over several continuous
functions) either is empty or carries full topological pressure. In particular,
if further the system is not uniquely ergodic, then the {\it
completely-irregular set}(i.e., intersection of all possible {\it nonempty
$\phi-$irregular} sets) is nonempty(even forms a dense $G_\delta$ set) and
carries full topological pressure. Moreover, {\it irregular-mix-regular sets}
(i.e., intersection of some $ \phi-$irregular sets and $ \varphi-$regular sets)
are discussed.
  Similarly, the above results are suitable for the case of BS-dimension.
  As consequences, these results are suitable for any system such as shifts of
finite type or uniformly hyperbolic diffeomorphisms, time-1 map of uniformly
hyperbolic flows, repellers, $\beta-$shifts etc..
