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- W2068457493 abstract "Our starting point is the proof of the following property of a particular class of matrices. Let T = { T i , j } be a n × m non-negative matrix such that ∑ j T i , j = 1 for each i . Suppose that for every pair of indices ( i , j ) , there exists an index l such that T i , l ≠ T j , l . Then, there exists a real vector k = ( k 1 , k 2 , … , k m ) T , k i ≠ k j , i ≠ j ; 0 < k i ⩽ 1 , such that, ( T k ) i ≠ ( T k ) j if i ≠ j . Then, we apply that property of matrices to probability theory. Let us consider an infinite sequence of linear functionals { T i } i ∈ N , T i f = ∫ f ( t ) d μ t ( i ) , corresponding to an infinite sequence of probability measures { μ ( · ) ( i ) } i ∈ N , on the Borel σ -algebra B ( [ 0 , 1 ] ) such that, μ ( · ) ( i ) ≠ μ ( · ) ( j ) , i , j ∈ N , i ≠ j . The property of matrices described above allows us to construct a real bounded one-to-one piecewise continuous and continuous from the left function f such that T i f = ∫ f ( t ) d μ t ( i ) ≠ ∫ f ( t ) d μ t ( j ) = T j f , i , j ∈ N , i ≠ j . The relevance to quantum mechanics is showed." @default.
- W2068457493 created "2016-06-24" @default.
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- W2068457493 date "2010-11-01" @default.
- W2068457493 modified "2023-10-16" @default.
- W2068457493 title "Stochastic matrices and a property of the infinite sequences of linear functionals" @default.
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- W2068457493 doi "https://doi.org/10.1016/j.laa.2010.05.006" @default.
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