In 1955, A. Revuz - Annales de l’Institut Fourier, vol. 6 (1955-56) - considered a type of Stieltjes measure defined on analogues of half-open, half-closed intervals in a partially ordered topological space. He states that these functions are finitely additive but his proof has an error. We shall furnish a new proof and extend some of this results to “measures” taking values in a topological abelian group.
An exponential inequality for Choquet expectation is discussed. We also obtain a strong law of large numbers based on Choquet expectation. The main results of this paper improve some previous results obtained by many researchers.
An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift of μ by a vector are neither equivalent nor orthogonal. This extends a result established in [7].