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Fill that measurable indicators are simple functions with the expected integral - #717

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Chessing234 wants to merge 4 commits into
teorth:mainfrom
Chessing234:feat/simple-function-indicators
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Fill that measurable indicators are simple functions with the expected integral#717
Chessing234 wants to merge 4 commits into
teorth:mainfrom
Chessing234:feat/simple-function-indicators

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Summary

  • A measurable indicator is an unsigned/real/complex simple function via a one-term representation.
  • The unsigned simple integral of that indicator is Lebesgue measure, by well-definedness of the simple integral.

Test plan

  • lake build Analysis.MeasureTheory.Section_1_3_1; CI covers the module.

Made with Cursor

This is the representation used by the unsigned simple-function calculus.
The on-set and off-set lemmas are used throughout the simple-function identities.
A one-term representation with coefficient one is the definition.
…asure.

Well-definedness of the simple integral reduces this to a one-term sum.
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