Gaussian isoperimetric inequality

In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov, and later independently by Christer Borell, states that among all sets of given Gaussian measure in the n-dimensional Euclidean space, half-spaces have the minimal Gaussian boundary measure. == Mathematical formulation == Let A {\displaystyle \scriptstyle A} be a measurable subset of R n {\displaystyle \scriptstyle \mathbf {R} ^{n}} endowed with the standard Gaussian measure γ n {\displaystyle \gamma ^{n}} with the density exp ⁡ ( − ‖ x ‖ 2 / 2 ) / ( 2 π ) n / 2 {\displaystyle {\exp(-\|x\|^{2}/2)}/(2\pi )^{n/2}} .

Source: Wikipedia — Gaussian isoperimetric inequality (CC BY-SA 4.0)

Gaussian isoperimetric inequality

In mathematics, the Gaussian isoperimetric inequality, proved by Boris Tsirelson and Vladimir Sudakov, and later independently by Christer Borell, states that among all sets of given Gaussian measure in the n-dimensional Euclidean space, half-spaces have the minimal Gaussian boundary measure. == Mathematical formulation == Let A {\displaystyle \scriptstyle A} be a measurable subset of R n {\displaystyle \scriptstyle \mathbf {R} ^{n}} endowed with the standard Gaussian measure γ n {\displaystyle \gamma ^{n}} with the density exp ⁡ ( − ‖ x ‖ 2 / 2 ) / ( 2 π ) n / 2 {\displaystyle {\exp(-\|x\|^{2}/2)}/(2\pi )^{n/2}} .

Source: Wikipedia "Gaussian isoperimetric inequality" · CC BY-SA 4.0

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