measure theory

"A theory that defines 'quantities' such as length, area, volume, and probability for very general spaces."

• Geometry → “shape”

• Topological space → "connection"

• Measure theory → "How much does it exist?"

1. Set XXX 2. σ-additive family (sigma algebra) 3. Measure μ\muμ

Fourier analysis

Quantum mechanics

Chaos theory

geometry

information theory

These connections lead to → probability theory → "designing density" → from "object" to "distribution field".

「空間内に何がどれくらい存在するかを見る」

Architecture is about "distribution," not "form."

Mathematical Architecture

space