34 lines
784 B
Plaintext
34 lines
784 B
Plaintext
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import Common.Geometry.Point
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import Common.Set.Partition
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/-! # Common.Geometry.StepFunction
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Characterization of step functions.
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-/
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namespace Geometry
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open Set Partition
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/--
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A function `f`, whose domain is a closed interval `[a, b]`, is a `StepFunction`
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if there exists a `Partition` `P = {x₀, x₁, …, xₙ}` of `[a, b]` such that `f` is
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constant on each open subinterval of `P`.
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-/
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structure StepFunction where
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p : Partition ℝ
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toFun : ∀ x ∈ p.toIcc, ℝ
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const_open_subintervals :
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∀ (hI : I ∈ p.openSubintervals), ∃ c, ∀ (hy : y ∈ I),
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toFun y (mem_open_subinterval_mem_closed_interval hI hy) = c
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namespace StepFunction
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/--
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The ordinate set of the function.
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-/
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def toSet (s : StepFunction) : Set Point := sorry
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end StepFunction
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end Geometry
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