content_image/302138.jpg content_image/302137.jpg content_image/302136.jpg content_image/302135.jpg
The fraction of observed counts in the cell C is a linear combination of empirical cumulative distribution functions 

<img src='content_image/302138.jpg'>

and the expected fraction under the null is a function of the marginal cumulative distributions 

<img src='content_image/302137.jpg'>

where ˆ F denotes the empirical distribution function based on N − ( m − 1) sample points. 

By the Glivenko-Cantelli theorem, uniformly almost surely, 

<img src='content_image/302136.jpg'>

Therefore, by Slutsky’s theorem and the continuous mapping theorem, we have that uniformly almost surely 

<img src='content_image/302135.jpg'>

