Learning.IT.adapted_obs
No docstring.
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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
MeasureTheory.Adapted (IT.filtration ๐ ๐ ๐จ) obsu is adapted to a filtration f if for all i, u i is f i-measurable.MeasurableSpace : Type u_6 โ Type u_6A measurable space is a space equipped with a ฯ-algebra.
MeasureTheory.Adapted : {ฮฉ : Type u_1} โ
{ฮน : Type u_2} โ
{m : MeasurableSpace ฮฉ} โ
[inst : Preorder ฮน] โ
{ฮฒ : ฮน โ Type u_3} โ
[(i : ฮน) โ MeasurableSpace (ฮฒ i)] โ MeasureTheory.Filtration ฮน m โ ((i : ฮน) โ ฮฉ โ ฮฒ i) โ PropA sequence of functions `u` is adapted to a filtration `f` if for all `i`, `u i` is `f i`-measurable. The definition known as `Adapted` before 2026-01-13 is now `StronglyAdapted`.
Learning.IT.filtration : (๐ : Type u_5) โ
(๐ : Type u_6) โ
(๐จ : Type u_7) โ
[inst : MeasurableSpace ๐] โ
[inst_1 : MeasurableSpace ๐] โ [inst_2 : MeasurableSpace ๐จ] โ MeasureTheory.Filtration โ inferInstanceFiltration of the algorithm Seq: `IT.filtration ๐ ๐ ๐จ n` is the ฯ-algebra generated by the rounds at times `0, ..., n`, that is by `hist (n + 1)`.Go to its page
Learning.IT.obs : {๐ : Type u_1} โ {๐ : Type u_2} โ {๐จ : Type u_3} โ โ โ (โ โ Learning.Round ๐ ๐ ๐จ) โ ๐`obs n` is the observation at time `n`. This is a random variable on the measurable space `โ โ Round ๐ ๐ ๐จ`.Go to its page
Code
lemma adapted_obs : Adapted (IT.filtration ๐ ๐ ๐จ) obs
Proof
by intro n rw [filtration_eq_comap, obs_eq_eval_comp_hist] exact measurable_comp_comap _ (by fun_prop)
New in v4.34.0-rc2-74-ge05e4f3 (2026-09-10), and its meaning has not changed since.
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: 4 project declarations, 11 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.