[Merged by Bors] - feat(MeasureTheory/VectorMeasure): add integral of a vector-valued function against a vector measure#28499
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This reverts commit e2b20d9.
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Co-authored-by: Etienne Marion <66847262+EtienneC30@users.noreply.github.com>
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| /-- `f : X → E` is said to be integrable with respect to `μ` and `B` if it is integrable with | ||
| respect to `(μ.transpose B).variation`. -/ | ||
| abbrev Integrable (μ : VectorMeasure X F) (B : E →L[ℝ] F →L[ℝ] G) (f : X → E) : Prop := |
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This should be protected to avoid namespace issues. Also, to match MeasureTheory.Integrable can you put f as the first argument please?
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done. should integral remain unprotected?
Co-authored-by: Etienne Marion <66847262+EtienneC30@users.noreply.github.com>
#min_imports, docstring
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I think it's good to go, thanks!
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I am not sure how |
Co-authored-by: Etienne Marion <66847262+EtienneC30@users.noreply.github.com>
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Thanks for your review! bors r+ |
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…nction against a vector measure (#28499) add `VectorMeasureWithPairing.integral` for normed vector spaces `E`, `F`, a Banach space `G` , a continuous linear pairing `B : E →L[ℝ] F →L[ℝ] → G` and an `F`-valued vector measure `μ`, which should be informally written as `∫ B (f x) ∂μ x`. motivation: there are natural vector measures such as signed measures and complex measures, and their integrals appear naturally e.g. in a proof of the spectral theorem for general bounded normal operators on a Hilbert space. - [x] depends on: #26160 for the definition and lemmas about the total variation of a vector measure. Co-authored-by: Oliver Butterley <oliver.butterley@gmail.com>
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…nction against a vector measure (leanprover-community#28499) add `VectorMeasureWithPairing.integral` for normed vector spaces `E`, `F`, a Banach space `G` , a continuous linear pairing `B : E →L[ℝ] F →L[ℝ] → G` and an `F`-valued vector measure `μ`, which should be informally written as `∫ B (f x) ∂μ x`. motivation: there are natural vector measures such as signed measures and complex measures, and their integrals appear naturally e.g. in a proof of the spectral theorem for general bounded normal operators on a Hilbert space. - [x] depends on: leanprover-community#26160 for the definition and lemmas about the total variation of a vector measure. Co-authored-by: Oliver Butterley <oliver.butterley@gmail.com>
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…nction against a vector measure (leanprover-community#28499) add `VectorMeasureWithPairing.integral` for normed vector spaces `E`, `F`, a Banach space `G` , a continuous linear pairing `B : E →L[ℝ] F →L[ℝ] → G` and an `F`-valued vector measure `μ`, which should be informally written as `∫ B (f x) ∂μ x`. motivation: there are natural vector measures such as signed measures and complex measures, and their integrals appear naturally e.g. in a proof of the spectral theorem for general bounded normal operators on a Hilbert space. - [x] depends on: leanprover-community#26160 for the definition and lemmas about the total variation of a vector measure. Co-authored-by: Oliver Butterley <oliver.butterley@gmail.com>
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VectorMeasureWithPairing.integralfor normed vector spacesE,F, a Banach spaceG, a continuous linear pairingB : E →L[ℝ] F →L[ℝ] → Gand anF-valued vector measureμ, which should be informally written as∫ B (f x) ∂μ x.motivation: there are natural vector measures such as signed measures and complex measures, and their integrals appear naturally e.g. in a proof of the spectral theorem for general bounded normal operators on a Hilbert space.