Fubini's Theorem for Daniell Integrals

Abstract: We show that for any two Daniell integrals

J

and

K

, given on some Riesz spaces

S

and

T

, there exists a product integral

I

on the space

R

, which is the smallest Riesz space containing the tensor product of

S

and

T

. The integral

I

is uniquely characterized by the property

I (f o t i m e s g) = J (f) K (g)

for all

f i n S

,

g i n T

. Also a Fubini-type theorem is presented.

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