## Lebesgue spaces. (Espaces de Lebesgue.)(French)Zbl 0788.60001

Azéma, J. (ed.) et al., Séminaire de probabilités XXVII. Berlin: Springer-Verlag. Lect. Notes Math. 1557, 15-21 (1993).
We give elementary proofs of some essential results concerning Lebesgue spaces. In particular, we prove the following well-known theorem: If a countable family of measurable sets separates points in a Lebesgue space, then it generates the whole $$\sigma$$-algebra. – For this, we give a new definition of a Lebesgue space, related to the inner regularity of a probability measure. Although equivalent to the one given by V. A. Rokhlin in his famous paper [Am. Math. Soc., Transl., II. Ser. 10, 2-53 (1962); translation from Math. Sb., N. Ser. 25(67), 107-150 (1949; Zbl 0033.169)], this definition turns out to be more convenient for the study of Lebesgue spaces.
For the entire collection see [Zbl 0780.00013].

### MSC:

 60A10 Probabilistic measure theory 60B05 Probability measures on topological spaces

Zbl 0033.169
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