The empirical method of Maurey

It is hard to define boundary mathematically. Zeta function is well known. ζ(s)=0

You need to fill all spaces for integration.

A⊂R^d

x is the convex hull of A.

When λn, n>d+1. Then, n-1 go to 0.

x2-x1=0.00000000000000000009. μ is the vector.

x1	x2	・・・・	xn
λ1(0.9)	λ11(0.00000000009)
λ2(0.09)	λ12(0.000000000009)
λ3(0.009)	λ13(0.0000000000009)
λ4(0.0009)	λ14(0.00000000000009)
λ5(0.00009)	λ15(0.000000000000009)
λ6(0.000009)	λ16(0.0000000000000009)
λ7(0.0000009)	λ17(0.00000000000000009)
λ8(0.00000009)	λ18(0.000000000000000009)
λ9(0.000000009)	λ19(0.0000000000000000009)
λ10(0.0000000009)	λ20(0.00000000000000000009)

λ10 is λ1 because of x1 which is the same group. You use Σ in your Excel. μ10 is also μ1. This is 0.0000000001. Then you keep expanding, but you close to Zero. However, you never reach Zero.

This is known as power law.