Friedgut's theorem for the continuous cube

Friedgut's theorem for the continuous cube

-
Hamed Hatami, Princeton University
Fine Hall 224

A celebrated theorem of Friedgut says that every boolean function on the discrete cube can be approximated by a function which depends only on a number of variables that depends on the sum of the influences of the variables of f. Dinur and Friedgut conjectured an analogue of this theorem for the continuous cube. I disprove their conjecture, and then prove the correct version of Friedgut's theorem for the continuous cube.