Measured creatures
  Using forcing with measured creatures we build a universe of set theory in which:   (a) every sup-measurable function f:RxR-->R is measurable, and   (b) every function f:R-->R is continuous on a non-measurable set.   This answers a question of Balcerzak, Ciesielski and Kharazishvili and von Weizsacker's problem (see Fremlin's list of problems). 
Andrzej Roslanowski and Saharon Shelah