几何测度论和调和分析的新近发展带来关于测度支集正则性的全新和深刻的成果。这些成果的一个显著特点在于它们根据测度的渐近行为实际刻画了支集的平坦性。这些特性引发了非光滑域上调和测度研究的重要的全新进展。
卢卡·卡波格纳、卡洛斯·E.肯尼格、洛伦达纳·兰扎尼著的《调和测度（几何与分析的观点英文版）（精）》提供了关于此领域研究文献的一个概览和导引，内容源于Carlos Kenig于2000年在阿肯色大学所做的阿肯色春季系列讲座中的五讲讲义。作者对原讲义做了扩充和更新，以反映这个领域的快速发展，增加的平面情形一章提供了一些历史背景。
书中包含了额外的背景知识介绍，使得调和分析和几何测度论方向的高年级研究生和研究人员能更好地理解本书的内容。

Introduction
Chapter 1.Motivation and statement of the main results
1.Characterization (1)α: Approximation with planes
2.Characterization (2)α: Introducing BMO and VMO
3.Multiplicative vs.additive formulation: Introducing the doubling condition
4.Characterization (1)α and flatness
5.Doubling and asymptotically optimally doubling measures
6.Regularity of a domain and doubling character of its harmonic measure
7.Regularity of a domain and smoothness of its Poisson kernel
Chapter 2.The relation between potential theory and geometry for planar domains
1.Smooth domains
2.Non smooth domains
3.Preliminaries to the proofs of Theorems 2.7 and 2.8
4.Proof of Theorem 2.7
5.Proof of Theorem 2.8
6.Notes
Chapter 3.Preliminary results in potential theory
1.Potential theory in NTA domains
2.A brief review of the real variable theory of weights
3.The spaces BMO and VMO
4.Potential theory in C1 domains
5.Notes
Chapter 4.Reifenberg flat and chord arc domains
1.Geometry of Reifenberg flat domains
2.Small constant chord arc domains
3.Notes
Chapter 5.Further results on Reifenberg fiat and chord arc domains
1.Improved boundary regularity for J-Reifenberg flat domains
2.Approximation and Rellich identity
3.Notes
Chapter 6.From the geometry of a domain to its potential theory
1.Potential theory for Reifenberg domains with vanishing constant
2.Potential theory for vanishing chord arc domains
3.Notes
Chapter 7.From potential theory to the geometry of a domain
1.Asymptotically optimally doubling implies Reifenberg vanishing
2.Back to chord arc domains
3.log k E VMO implies vanishing chord arc; Step I
4.log k E VMO implies vanishing chord arc; Step II
5.Notes
Chapter 8.Higher codimension and further regularity results
1.Notes
Bibliography