Abstract
For each sequence of points in a compactF-spaceX the corresponding sequence of Cesàro sums (1/n)Σ n i=1 f(x i ) diverges for somef inC(X). It follows that each minimal set in a discrete flow (X, h) supports at least two ergodich-invariant Borel probability measures.
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Gait, J., Koo, SC. Averages of functions and ergodic measures inF-spaces. Math. Systems Theory 6, 23–25 (1972). https://doi.org/10.1007/BF01706071
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DOI: https://doi.org/10.1007/BF01706071