5,337
edits
Line 769: | Line 769: | ||
Consider the compliment <math>R^c</math>. | Consider the compliment <math>R^c</math>. | ||
The area of the complement is <math>u_1(R^c) \geq \frac{1}{2}</math>. | The area of the complement is <math>u_1(R^c) \geq \frac{1}{2}</math>. | ||
The area of the epsilon expansion is <math>u_1(R^c(\epsilon)) \geq 1 - (\pi/8)^{1/2} \exp(-\frac{d-1}{2}\epsilon^2 | The area of the epsilon expansion is <math>u_1(R^c(\epsilon)) \geq 1 - (\pi/8)^{1/2} \exp(-\frac{d-1}{2}\epsilon^2)</math>. Thus the ''safe zone'' is very small in high dimension. | ||
;Lemma | ;Lemma |