measurable_sigma_of_measurable_comp_mk
From the authors
A function on a sigma type is measurable if all its restrictions to the fibers are.
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α : Type u_1 -
γ : Type u_2MeasurableSpace γA measurable space is a space equipped with a σ-algebra.
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β : α → Type u_3(a : α) → MeasurableSpace (β a) -
f : (a : α) × β a → γ
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h : ∀ (a : α), Measurable (f ∘ Sigma.mk a)A functionfbetween measurable spaces is measurable if the preimage of every measurable set is measurable.
Measurable fMeasurableSpace : Type u_6 → Type u_6A measurable space is a space equipped with a σ-algebra.
Measurable : {α : Type u_1} → {β : Type u_2} → [MeasurableSpace α] → [MeasurableSpace β] → (α → β) → PropA function `f` between measurable spaces is measurable if the preimage of every measurable set is measurable.
Function.comp : {α : Sort u} → {β : Sort v} → {δ : Sort w} → (β → δ) → (α → β) → α → δFunction composition, usually written with the infix operator `∘`. A new function is created from two existing functions, where one function's output is used as input to the other. Examples: * `Function.comp List.reverse (List.drop 2) [3, 2, 4, 1] = [1, 4]` * `(List.reverse ∘ List.drop 2) [3, 2, 4, 1] = [1, 4]` Conventions for notations in identifiers: * The recommended spelling of `∘` in identifiers is `comp`.
Sigma.mk : {α : Type u} → {β : α → Type v} → (fst : α) → β fst → Sigma βConstructs a dependent pair. Using this constructor in a context in which the type is not known usually requires a type ascription to determine `β`. This is because the desired relationship between the two values can't generally be determined automatically.
Code
lemma measurable_sigma_of_measurable_comp_mk {f : (Σ a, β a) → γ}
(h : ∀ a, Measurable (f ∘ Sigma.mk a)) : Measurable fProof
fun _ hs ↦ measurableSet_iInf.2 fun a ↦ (h a) hs
New in v4.34.0-rc2-82-ga6c27a7 (2026-09-13), 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, 6 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.