Learning.IT.measurable_hist_filtrationAction
Lemma
No docstring.
Types
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๐ : Type u_1m๐ : MeasurableSpace ๐A measurable space is a space equipped with a ฯ-algebra. -
๐ : Type u_2m๐ : MeasurableSpace ๐ -
๐จ : Type u_3m๐จ : MeasurableSpace ๐จ
Given
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n : โ
Then
Measurable (hist n)f between measurable spaces is measurable if the preimage of every measurable set is measurable.MeasurableSpace : Type u_6 โ Type u_6A measurable space is a space equipped with a ฯ-algebra.
Nat : TypeThe natural numbers, starting at zero. This type is special-cased by both the kernel and the compiler, and overridden with an efficient implementation. Both use a fast arbitrary-precision arithmetic library (usually [GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.
Measurable : {ฮฑ : Type u_1} โ {ฮฒ : Type u_2} โ [MeasurableSpace ฮฑ] โ [MeasurableSpace ฮฒ] โ (ฮฑ โ ฮฒ) โ PropA function `f` between measurable spaces is measurable if the preimage of every measurable set is measurable.
Learning.IT.hist : {๐ : Type u_1} โ {๐ : Type u_2} โ {๐จ : Type u_3} โ (n : โ) โ (โ โ Learning.Round ๐ ๐ ๐จ) โ Learning.Hist ๐ ๐ ๐จ n`hist n` is the history before time `n`: the rounds at times `0, ..., n - 1`. This is a random variable on the measurable space `โ โ Round ๐ ๐ ๐จ`.Go to its page
Code
lemma measurable_hist_filtrationAction (n : โ) :
Measurable[filtrationAction ๐ ๐ ๐จ n] (hist n)Proof
(measurable_fst.comp measurable_fst).comp (measurable_iff_comap_le.mpr le_rfl)
Meaning last changed in v4.34.0-rc2-74-ge05e4f3 (2026-09-10).
Self-contained, with its dependencies inlined and proofs replaced by sorry: download the raw file ยท open it in the Lean web editor.
Dependency graph
Audit surface: 8 project declarations, 17 external constants
โ Proved: no sorry anywhere in its closure
This is the tool's own reading of one build's recorded axioms, and it is not robust against an author who wants it to pass. Checking meant to be relied on should go through Comparator, which replays the proof through the kernel from an export against an explicit list of permitted axioms.