The Surface Measure and Cone Measure on the sphere of `p
نویسنده
چکیده
We prove a concentration inequality for the `q norm on the `p sphere for p, q > 0. This inequality, which generalizes results of Schechtman and Zinn, is used to study the distance between the cone measure and surface measure on the sphere of `p . In particular, we obtain a significant strengthening of the inequality derived in [NR], and calculate the precise dependence of the constants that appeared there on p.
منابع مشابه
Projecting the Surface Measure of the Sphere Of
– We prove that the total variation distance between the cone measure and surface measure on the sphere of p is bounded by a constant times 1/ √ n. This is used to give a new proof of the fact that the coordinates of a random vector on the p sphere are approximately independent with density proportional to exp(−|t|p), a unification and generalization of two theorems of Diaconis and Freedman. Fi...
متن کاملChange of diffused and scattered light with surface roughness of p-type porous Silicon
Porous silicon samples were prepared by electrochemical etching method for different etching times. The structural properties of porous silicon (PS) samples were determined from the Atomic Force Microscopy (AFM) measurements. The surface mean root square roughness (σ rms) changes as function of porosity were studied, and the influence of etching time on porosity and roughness was studied too. U...
متن کاملChange of diffused and scattered light with surface roughness of p-type porous Silicon
Porous silicon samples were prepared by electrochemical etching method for different etching times. The structural properties of porous silicon (PS) samples were determined from the Atomic Force Microscopy (AFM) measurements. The surface mean root square roughness (σ rms) changes as function of porosity were studied, and the influence of etching time on porosity and roughness was studied too. U...
متن کاملEgoroff Theorem for Operator-Valued Measures in Locally Convex Cones
In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...
متن کاملIntroducing Capacity Surface to Estimate Watermarking Capacity
One of the most important parameters in evaluating a watermarking algorithm is its capacity. Generally, watermarking capacity is expressed by bits per pixel (bpp) unit measure. But this measure does not show what the side effects would be on image quality, watermark robustness and capacity. In this paper we propose a three dimensional measure named Capacity surface which shows the effects of ca...
متن کامل