Exact(1)
If the integrand is a continuous (mathbf {R}^{n} -valued function over a path-connected topological space, we prove that any such integral can be represented as a convex combination of values of the integrand in at most n points, which yields an ultimate multivariate mean value theorem.
Similar(7)
The multivariate-adjusted mean value for the GFR slope decreased significantly faster in subjects with four or more MetS components in comparison with those who had one or no components, and the mean of the GFR slope showed a significantly greater decline in subjects with three MetS components in the group 60 years and older.
The age- and sex-adjusted or multivariate-adjusted mean values for log-transformed HbA1c were calculated by an ANCOVA, back-transformed, and reported as adjusted geometric means and their 95% CIs.
As a direct corollary to Theorems 2.10 and 3.2, we have the following mean value theorem for continuous multivariate mappings.
Multivariate gene expression data is characterised by its mean value structure as well as its dependence or correlation structure.
In multivariate case, with (Xin mathbf {R}^{n}), (ngeq1), there is an old and seemingly forgotten mean value theorem by Kowalewski [1, 2] as follows.
value Mean value Std.
The mean value (s.d).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com