All Questions

Let $X,Y$ be probability measures on $\{1,2,\dots,n\}$, and set $K=\sum_i\sqrt{X(i)Y(i)}$ so that $Z:=\frac{1}{K}\sqrt{XY}$ is also a probability measure on $\{1,2,\dots,n\}$. How can we prove the ...

My question comes from understanding a probabilistic inequality in Bourgain's paper on Erdős simiarilty problem: Construction of sets of positive measure not containing an affine image of a given ...