in analysis we defined measurable function as functions so that the preimages of intervalls are measureable which is equivalent to that preimages of borel sets are measureable.
in probabilty theory we defined measureable functions as functions so that preimages of all _measureable_ sets are measureable, which leads to some (for me bigger) differences, e.g. in analysis the chaining of two measureable functions doesn't need to be measureable, in probability theory though it does.
is it normal that there are two different definitions for something so basic?
