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Give an example of a subset of R that is not a Borel set?
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 = =
Is the inverse image of a measurable set under a continuous map measurable?
Yes, the inverse image of a measurable set under a continuous map is measurable. If ( f: X \to Y ) is a continuous function and ( A \subseteq Y ) is a measurable set, then the preimage ( f^{-1}(A) ) is measurable in ( X ). This property holds for various types of measurable spaces, including Borel and Lebesgue measurability. Thus, continuous functions preserve the measurability of sets through their inverse images.
What is the birth name of Annik Borel?
Annik Borel's birth name is Borel, Anne.
What is the birth name of Louis Borel?
Louis Borel's birth name is Lodewijk Borel.
When was Ernest Borel created?
Ernest Borel was created in 1856.
When did Adrien Borel die?
Adrien Borel died in 1966.
When was Adrien Borel born?
Adrien Borel was born in 1886.
When was Frédéric Borel born?
Frédéric Borel was born in 1959.
When did Petrus Borel die?
Petrus Borel died in 1859.
When was Petrus Borel born?
Petrus Borel was born in 1809.
When did Felice Borel die?
Felice Borel died in 1993.
When was Daniel Borel born?
Daniel Borel was born in 1950.
