Harmonic measure

Harmonic measure is a concept in mathematics that describes how a boundary influences the behavior of a process like heat or electric potential inside a domain. Imagine placing a source at the boundary of a region and observing how its effect (like temperature) spreads inward; the harmonic measure tells us the likelihood that a random path starting inside will exit the domain near a specific point on the boundary. It effectively quantifies the boundary's impact on interior points, helping us understand phenomena like diffusion, potential flow, or probability distributions in complex shapes.