Characteristic function of any borel set is an example of simple Borel function
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∙ 11y agoOne example of a simple Borel measurable function is the indicator function of a Borel set. This function takes the value 1 on the set and 0 outside the set, making it easy to determine its measurability with respect to the Borel sigma algebra.
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 = =
Louis Borel's birth name is Lodewijk Borel.
Annik Borel's birth name is Borel, Anne.
Frédéric Borel was born in 1959.
Jacques Borel died in 2002.
Jacques Borel was born in 1925.
Felice Borel died in 1993.
Petrus Borel died in 1859.
Petrus Borel was born in 1809.
Ernest Borel was created in 1856.
Daniel Borel was born in 1950.
Pierre Borel died in 1689.