Article Dans Une Revue The Mathematical Intelligencer Année : 2025

An extension of the mean value theorem

Résumé

Let (Ω, µ) be a measure space with Ω ⊂ R d and µ a finite measure on Ω. We provide an extension of the Mean Value Theorem (MVT) in the form

It is valid for non compact sets Ω and f is only required to be integrable with respect to µ. It also contains as a special case the MVT in the form f dµ = µ(Ω)f (x 0 ) for some x 0 ∈ Ω, valid for compact connected set Ω and continuous f . It is a direct consequence of Richter's theorem which in turn is a non trivial (overlooked) generalization of Tchakaloff's theorem, and even published earlier.

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Dates et versions

hal-05289719 , version 1 (30-09-2025)

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Jean B Lasserre. An extension of the mean value theorem. The Mathematical Intelligencer, 2025, 4 p. ⟨10.1007/s00283-025-10471-5⟩. ⟨hal-05289719⟩
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