of functions from
satisfying the following conditions:
is a vector space
contains the continuous functions
is an increasing sequence of nonnegative functions in
exists and is finite for all
Show that the collection
consisting of the Borel-measurable functions is the smallest such collection of functions. (Hint: define
. Show that
contains the interval
, and then contains the Borel sets).
characteristic function of
I show that
, but i try prove
is a sigma-algebra but the union countable give me troubles, some help for it?
any help is apreciated, my first post