measurable_sigma_mk
No docstring.
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α : Type u_1
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β : α → Type u_3(a : α) → MeasurableSpace (β a)A measurable space is a space equipped with a σ-algebra. -
a : α
Measurable (Sigma.mk a)f between measurable spaces is measurable if the preimage of every measurable set is measurable.MeasurableSpace : 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.
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_mk (a : α) : Measurable (Sigma.mk a : β a → Σ a, β a)
Proof
fun _ hs ↦ measurableSet_iInf.1 hs a
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, 5 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.