A functional from geometry with applications to discrepancy estimates and the Radon transform

Rogers, Allen D.

doi:10.1090/S0002-9947-1994-1169082-8

A functional from geometry with applications to discrepancy estimates and the Radon transform
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Trans. Amer. Math. Soc. 341 (1994), 275-313 Request permission

Abstract:

Estimates of discrepancy, or irregularities of distribution, are obtained for measures without atoms. Two estimators are used, the half-space, or separation, discrepancy ${D_S}$ and a geometric functional ${I^\alpha }$. A representation formula for the generalized energy integral ${I^\alpha }$ is developed. Norm inequalities for the Radon transform are obtained as an application of the continuous discrepancy results. Integral geometric notions play a prominent role.

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