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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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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 (

Keywords: Resolvents, Strong Feller properties

Nature: Exposition

Retrieve article from Numdam