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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 Daniel Borel born?
Daniel Borel was born in 1950.
When did Jacques Borel die?
Jacques Borel died in 2002.
When was Jacques Borel born?
Jacques Borel was born in 1925.
When did Felice Borel die?
Felice Borel died in 1993.
When did Pierre Borel die?
Pierre Borel died in 1689.
When was Pierre Borel born?
Pierre Borel was born in 1620.
When did Petrus Borel die?
Petrus Borel died in 1859.
When was Petrus Borel born?
Petrus Borel was born in 1809.
