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Math and science::Analysis::Tao, measure::02. Lebesgue measure

Lebesgue measurable sets.

The following sets meet the criteria to be Lebesgue measurable:

  1. Every [...] set is Lebesgue measurable.
  2. A countable [...] of Lebesgue measurable sets is Lebesgue measurable.
  3. Every [...] set is Lebesgue measurable.
  4. The [c________] of a Lebesgue measurable set \( E \) is Lebesgue measurable.
  5. A countable [...] of Lebesgue measurable sets is Lebesgue measurable.

Two others are:

  • Every set of Lebesgue outer measure [...] is measurable. These sets are called [...] sets.
  • The empty set \( \emptyset \) is Lebesgue measurable.

The proofs are on the reverse side, along with a repeat of the definition of Lebesgue measurability.