# This script creates a plot of a cdf which is continuous but not absolutely
# continuous.

# The cdf increases only on the Cantor set.

cdfinv<-function(x,k=32){
y<-matrix(0,length(x),k)
for(i in 1:k){
x<-2*x
y[,i]<-floor(x)
x<-x-y[,i]
}
2*as.numeric(y%*%3^(-(1:k)))
}

y<-seq(0,1,length=1e6+1)[-(1e6+1)]
x<-cdfinv(y)
plot(x,y,type="l",main="CDF which is continuous but NOT absolutely continuous")