Commit 2025-09-30 12:55 b34acd39

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feat(Analysis/SpecialFunctions): add the sigmoid function (#28780) Add the Sigmoid from to and from to I and show some analytical properties. Then, add sigmoid_ord_embedding, the Sigmoid function seen as an OrderEmbedding from to I. Show that it is a MeasurableEmbedding and that we could use it to construct a MeasurableEmbedding from any StandardBorelSpace to I.

Estimated changes

added theorem AnalyticAt.sigmoid'
added theorem AnalyticAt.sigmoid
added theorem AnalyticOn.sigmoid
added theorem AnalyticOnNhd.sigmoid
added theorem ContDiff.sigmoid
added theorem Continuous.sigmoid
added theorem Differentiable.sigmoid
added theorem Real.deriv_sigmoid
added theorem Real.range_sigmoid
added theorem Real.sigmoid_def
added theorem Real.sigmoid_inj
added theorem Real.sigmoid_injective
added theorem Real.sigmoid_le
added theorem Real.sigmoid_le_iff
added theorem Real.sigmoid_le_one
added theorem Real.sigmoid_lt
added theorem Real.sigmoid_lt_iff
added theorem Real.sigmoid_lt_one
added theorem Real.sigmoid_monotone
added theorem Real.sigmoid_neg
added theorem Real.sigmoid_nonneg
added theorem Real.sigmoid_pos
added theorem Real.sigmoid_zero
added theorem analyticAt_sigmoid
added theorem analyticOnNhd_sigmoid
added theorem analyticOn_sigmoid
added theorem contDiff_sigmoid
added theorem continuous_sigmoid
added theorem differentiable_sigmoid