Full length article On Chebyshev–Markov–Krein inequalities

We review the topic of Chebyshev–Markov–Krein inequalities, i.e. estimates for inf f dν and sup f dν ν∈V (µ) ν∈V (µ) where µ is a non-negative finite measure, and V (µ) is the set of all non-negative finite measures ν satisfying u dν = u dµ for all u ∈ U, where U is a finite-dimensional subspace. For U a finite-dimensional T-space on [a, b], we prove correct necessary and sufficient conditions for when a given non-negative function f ∈ C[a, b] satisfies � ξ − � ξ − � ξ+ � ξ+ f dµξ ≤ f dν ≤ f dν ≤ f dµξ a