significant observational progress has been made in the measurement of the SMF of galaxies and its evolution with redshift. Using photometric redshifts derived from multi-waveband imaging surveys, measurements of the SMF of galaxies are now routinely performed out to $z\sim5$ (e.g., @dickinson03; @conselice05; @drory05; @fontana06; @elsner08; @perez08; @kajisawa09; @marchesini09). The general consensus is that at $z>1$ the stellar mass assembly proceeds much more quickly than at lower redshifts. In particular, very recent measurements at $z<4$ show a dramatic evolution of the SMF of galaxies with redshift as well as evidence of mass-dependent evolution of the SMF, with the low-mass end evolving more rapidly than the high-mass end (i.e., @perez08; @marchesini09).

Measurements of the SMF have been extended also to even larger redshifts ($z\sim$4-7; e.g., @mclure09; @stark09), providing estimates of the stellar mass content of the universe when it was only $\sim$800 Myr old. However, most of these studies only target Lyman break galaxies (LBGs), hence resulting in a potentially biased view of the universe against massive and evolved galaxies at such high redshifts. Whereas the discovery of a population of very massive and evolved galaxies at $z\ga 5$ has now been claimed by several groups (e.g., @yan06; @rodighero07; @wiklind08; @mancini09), 