ProbabilityTheory.instMeasurableSpaceKernel
No docstring.
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𝓧 : Type u_1m𝓧 : MeasurableSpace 𝓧A measurable space is a space equipped with a σ-algebra. -
𝓨 : Type u_2m𝓨 : MeasurableSpace 𝓨
MeasurableSpace (Kernel 𝓧 𝓨)MeasurableSpace.comap (fun κ => ⇑κ) inferInstanceMeasurableSpace : Type u_6 → Type u_6A measurable space is a space equipped with a σ-algebra.
ProbabilityTheory.Kernel : (α : Type u_1) → (β : Type u_2) → [MeasurableSpace α] → [MeasurableSpace β] → Type (max u_1 u_2)A kernel from a measurable space `α` to another measurable space `β` is a measurable function `κ : α → Measure β`. The measurable space structure on `MeasureTheory.Measure β` is given by `MeasureTheory.Measure.instMeasurableSpace`. A map `κ : α → MeasureTheory.Measure β` is measurable iff `∀ s : Set β, MeasurableSet s → Measurable (fun a ↦ κ a s)`.
MeasurableSpace.comap : {α : Type u_1} → {β : Type u_2} → (α → β) → MeasurableSpace β → MeasurableSpace αThe reverse image of a measurable space under a function. `comap f m` contains the sets `s : Set α` such that `s` is the `f`-preimage of a measurable set in `β`.
inferInstance : {α : Sort u} → [i : α] → α`inferInstance` synthesizes a value of any target type by typeclass inference. This function has the same type signature as the identity function, but the square brackets on the `[i : α]` argument means that it will attempt to construct this argument by typeclass inference. (This will fail if `α` is not a `class`.) Example: ``` #check (inferInstance : Inhabited Nat) -- Inhabited Nat def foo : Inhabited (Nat × Nat) := inferInstance example : foo.default = (default, default) := rfl ```
Code
instance instMeasurableSpaceKernel : MeasurableSpace (Kernel 𝓧 𝓨)
Proof
MeasurableSpace.comap (fun κ ↦ (κ : 𝓧 → Measure 𝓨)) inferInstance
New in v4.34.0-rc2-78-g3ff93c0 (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 · open it in the Lean web editor.
Dependency graph
Nothing to draw. Its statement rests on no other declaration in this project, and names nothing from a package left unaudited — so the graph is this declaration alone. That is the answer, not a missing picture.
Audit surface: 0 project declarations, 9 external constants
✓ 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.