Can someone explain the formulae highlighted (yellow) on page 5 in attached file?

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David Eugene Booth

Sunita, This paper involves a dose of both measure theory and functional analysis both of which I studied 40 years ago. I suggest that you contact Billard directly:

https://en.wikipedia.org/wiki/Lynne_Billard

and

http://www.stat.uga.edu/directory/people/lynne-billard

Best wishes, David Booth

Sunita Guru

Thanks David.

Venkatesh Gauri Shankar

You can Find answer with explanation and also future queries in given books:

There are three main textbooks: ##Bock, H.H., Diday, E. (2000) Analysis of Symbolic Data, Exploratory methods for extracting statistical information from complex data. Studies in Classification, Data Analysis and Knowledge Organisation, Springer-Verlag. ##Symbolic Data Analysis and the SODAS Software, Edwin Diday (Editor), Monique Noirhomme-Fraiture (Editor) , wiley 2008.