Analysis

Learn Geometric Measure Theory

Surfaces built out of measure theory, so that a minimiser exists before anyone knows it is smooth. Covers Hausdorff measure and rectifiability, the area and coarea formulas, sets of finite perimeter, currents and varifolds, and why regularity holds up to dimension eight and fails after it.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Geometric Measure Theory

Hausdorff measureBox dimension and contentDensities and density pointsThe Besicovitch covering theoremLipschitz maps and Rademacher's theoremThe area formulaThe coarea formulaRectifiable setsPurely unrectifiable setsTangent measuresSets of finite perimeterDe Giorgi's structure theoremIsoperimetry and Brunn-MinkowskiPlateau's problemCurrents, mass and flat normThe Federer-Fleming compactness theoremVarifolds and first variationRegularity and the singular set
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Geometric Measure Theory exactly where it's useful.

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