{"ID":2861346,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.01726","arxiv_id":"2510.01726","title":"An extension of the mean value theorem","abstract":"Let ($Ω$, $μ$) be a measure space with $Ω$ $\\subset$ 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 d$μ$ = $μ$($Ω$)f (x 0 ) for some x 0 $\\in$ $Ω$, 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.","short_abstract":"Let ($Ω$, $μ$) be a measure space with $Ω$ $\\subset$ 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 d$μ$ =...","url_abs":"https://arxiv.org/abs/2510.01726","url_pdf":"https://arxiv.org/pdf/2510.01726v1","authors":"[\"Jean B Lasserre\"]","published":"2025-10-02T07:08:49Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}