Let: $$G=\left\{x\in \mathbb R^n: x=(x_1,...,x_{n-1},0) \right\},$$ $S$ - cone based on the set $A\subset G$ which is bounded set, $$A'=\left\{x'\in \mathbb R^{n-1}: x'=(x_1,...,x_{n-1}) \right\}, \lambda_{n-1}(A')<\infty$$Moreover assume that the tip of the cone $S$ lies at a distance $g$ from $G$.

What is the distance from $G$ to centre of gravity set $S$?

If $A\subset \mathbb R^n$ is a measurable set then the point $x=(x_1,...,x_n)$ where $x_i=\frac{1}{\lambda_n(A)} \int_A y_i d \lambda(y_1,y_2,...,y_n)$ is the centre of gravity.

But I don't know how to use this knowledge to do this task.

Can you help me?


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