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MeasureTheory.MeasurableSpace.Basic
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/- | ||
Copyright (c) 2017 Johannes Hölzl. All rights reserved. | ||
Released under Apache 2.0 license as described in the file LICENSE. | ||
Authors: Johannes Hölzl, Mario Carneiro | ||
-/ | ||
import Mathlib.MeasureTheory.MeasurableSpace.Defs | ||
import Mathlib.Data.Rat.Init | ||
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#align_import measure_theory.measurable_space from "leanprover-community/mathlib"@"001ffdc42920050657fd45bd2b8bfbec8eaaeb29" | ||
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/-! | ||
# Measurable-space typeclass instances | ||
This file provides measurable-space instances for a selection of standard countable types, | ||
in each case defining the Σ-algebra to be `⊤` (the discrete measurable-space structure). | ||
-/ | ||
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instance Empty.instMeasurableSpace : MeasurableSpace Empty := ⊤ | ||
#align empty.measurable_space Empty.instMeasurableSpace | ||
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instance PUnit.instMeasurableSpace : MeasurableSpace PUnit := ⊤ | ||
#align punit.measurable_space PUnit.instMeasurableSpace | ||
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instance Bool.instMeasurableSpace : MeasurableSpace Bool := ⊤ | ||
#align bool.measurable_space Bool.instMeasurableSpace | ||
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instance Prop.instMeasurableSpace : MeasurableSpace Prop := ⊤ | ||
#align Prop.measurable_space Prop.instMeasurableSpace | ||
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instance Nat.instMeasurableSpace : MeasurableSpace ℕ := ⊤ | ||
#align nat.measurable_space Nat.instMeasurableSpace | ||
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instance Fin.instMeasurableSpace (n : ℕ) : MeasurableSpace (Fin n) := ⊤ | ||
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instance Int.instMeasurableSpace : MeasurableSpace ℤ := ⊤ | ||
#align int.measurable_space Int.instMeasurableSpace | ||
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instance Rat.instMeasurableSpace : MeasurableSpace ℚ := ⊤ | ||
#align rat.measurable_space Rat.instMeasurableSpace | ||
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instance Subsingleton.measurableSingletonClass {α} [MeasurableSpace α] [Subsingleton α] : | ||
MeasurableSingletonClass α := by | ||
refine ⟨fun i => ?_⟩ | ||
convert MeasurableSet.univ | ||
simp [Set.eq_univ_iff_forall, eq_iff_true_of_subsingleton] | ||
#noalign empty.measurable_singleton_class | ||
#noalign punit.measurable_singleton_class | ||
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instance Bool.instMeasurableSingletonClass : MeasurableSingletonClass Bool := ⟨fun _ => trivial⟩ | ||
#align bool.measurable_singleton_class Bool.instMeasurableSingletonClass | ||
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instance Prop.instMeasurableSingletonClass : MeasurableSingletonClass Prop := ⟨fun _ => trivial⟩ | ||
#align Prop.measurable_singleton_class Prop.instMeasurableSingletonClass | ||
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instance Nat.instMeasurableSingletonClass : MeasurableSingletonClass ℕ := ⟨fun _ => trivial⟩ | ||
#align nat.measurable_singleton_class Nat.instMeasurableSingletonClass | ||
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instance Fin.instMeasurableSingletonClass (n : ℕ) : MeasurableSingletonClass (Fin n) := | ||
⟨fun _ => trivial⟩ | ||
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instance Int.instMeasurableSingletonClass : MeasurableSingletonClass ℤ := ⟨fun _ => trivial⟩ | ||
#align int.measurable_singleton_class Int.instMeasurableSingletonClass | ||
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instance Rat.instMeasurableSingletonClass : MeasurableSingletonClass ℚ := ⟨fun _ => trivial⟩ | ||
#align rat.measurable_singleton_class Rat.instMeasurableSingletonClass |
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