Geodesic
Equivalence between distribution functions and probability measures on a LOTS
Filomat, Tome 35 (2021) no. 14, p. 4657

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DOI

In this paper we give some conditions such that there is an equivalence between probability measures and distribution functions defined on a separable linearly ordered topological space like it happens in the classical case. What is more, we prove that there is a one-to-one relationship between a probability measure and the pseudo-inverse of its cumulative distribution function
DOI : 10.2298/FIL2114657G
Classification : 60E05, 60B05
Keywords: Probability, measure, cut, Dedekind-MacNeille completion, linearly ordered topological space, outer measure, σ-algebra, Borel σ-algebra, cumulative distribution function, sample 
José Fulgencio Gálvez-Rodríguez; Migueí Angel Sánchez-Granero. Equivalence between distribution functions and probability measures on a LOTS. Filomat, Tome 35 (2021) no. 14, p. 4657 . doi: 10.2298/FIL2114657G
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     author = {Jos\'e Fulgencio G\'alvez-Rodr{\'\i}guez and Migue{\'\i} Angel S\'anchez-Granero},
     title = {Equivalence between distribution functions and probability measures on a {LOTS}},
     journal = {Filomat},
     pages = {4657 },
     year = {2021},
     volume = {35},
     number = {14},
     doi = {10.2298/FIL2114657G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2114657G/}
}
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