Joint Measurability and the One-way Fubini Property for a Continuum of Independent Random Variables
نویسندگان
چکیده
As is well known, a continuous parameter process with mutually independent random variables is not jointly measurable in the usual sense. This paper proposes an extension of the usual product measure-theoretic framework, using a natural “one-way Fubini” property. When the random variables are independent even in a very weak sense, this property guarantees joint measurability and defines a unique measure on a suitable minimal σ-algebra. However, a further extension to satisfy the usual (two-way) Fubini property, as in the case of Loeb product measures, may not be possible in general. Some applications are also given.
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