Characteristic function of any borel set is an example of simple Borel function
An example is given here: http://en.wikipedia.org/wiki/Non-Borel_set Any set that is easy to think of will be a Borel set, so an example of a non-Borel set will be complicated. Another approach: All Borel sets are Lebesgue measurable. The axiom of choice can be used to give an example of a non-measurable set, and this set will also be a non-Borel set. See http://en.wikipedia.org/wiki/Non-measurable_set = =
Annik Borel's birth name is Borel, Anne.
Louis Borel's birth name is Lodewijk Borel.
Daniel Borel was born in 1950.
Jacques Borel died in 2002.
Jacques Borel was born in 1925.
Felice Borel died in 1993.
Pierre Borel died in 1689.
Pierre Borel was born in 1620.
Petrus Borel died in 1859.
Petrus Borel was born in 1809.
Frédéric Borel was born in 1959.