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II: 10, 171-174, LNM 51 (1968)
MEYER, Paul-André
Les résolvantes fortement fellériennes d'après Mokobodzki (Potential theory)
On a compact space, a submarkov kernel $N$ has the strong Feller property if it maps Borel bounded functions into continuous functions, and the stronger Feller property if the mapping $x\rightarrow \epsilon_x N$ is continuous in the norm topology of measures. It is proved that the product of two strong Feller kernels is stronger Feller, and as a consequence if the kernels of are resolvent are strong Feller they are automatically stronger Feller
Comment: This follows from a result on weakly compact operators on continuous functions due to Grothendieck (Canadian J. Math., 5, 1953). Mokobodzki's proof is less general (it uses positivity) but very simple. This result is rather useful
Keywords: Resolvents, Strong Feller properties
Nature: Exposition
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