# Proof of an Intersection Theorem via Fourier Analysis

### Ehud Friedgut

Hebrew University, Jerusalem, Israel

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## Abstract

Let p ≤ ½ and let μp be the product measure on {0,1}n, where μp(x) = p∑xi (1 − p)n − ∑xi. Let **A** ⊂ {0,1}n be an intersecting family, i.e., for every x, y ∈ **A** there exists 1 ≤ i ≤ n such that xi = yi = 1. Then μp(**A**) ≤ p. The proof uses discrete harmonic analysis.