On the Representation of Doubly Stochastic Integral Operators by Means of Disjoint Isomorphisms

  • V. N. Sudakov
Part of the Seminars in Mathematics book series (SM)


A doubly stochastic integral operator is an integral operator of the form
$$\left( {Bf} \right)\left( y \right) = \int\limits_X {k\left( {x,y} \right)f\left( x \right)d\mu \left( x \right)} ,$$
pwhere k (x,y) is a negative function given on the product M =X × Y of spaces with measures (X,μ) and (Y,v), where \(\int\limits_X {k\left( {x,y} \right)d\mu \left( x \right)} = 1\) for almost all y ∈ Y and \(\int\limits_Y {k\left( {x,y} \right)dv\left( y \right)} = 1\) for almost all x∈X.


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© Springer Science+Business Media New York 1972

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  • V. N. Sudakov

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