integrable_continuousLinearMap_prod

English

If L is a continuous linear map on E×F→G and the two component maps are integrable, then L is integrable on μ×ν.

Русский

Если L — непрерывное линейное отображение E×F→G и обе компоненты интегрируемы, то L интегрируемо на μ×ν.

LaTeX

$$$$\\text{Integrable } L \\text{ on } μ×ν $$$$

Lean4

theorem integrable_continuousLinearMap_prod (hμ : Integrable id μ) (hν : Integrable id ν) : Integrable L (μ.prod ν) :=
  integrable_continuousLinearMap_prod' (ContinuousLinearMap.integrable_comp _ hμ)
    (ContinuousLinearMap.integrable_comp _ hν)

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