Previsions are positively homogeneous functionals, and are generalized forms of integration functionals. We investigate previsions -- just previsions, not sublinear or superlinear previsions as in previous work. We show that every prevision can be expressed as an infimum of sublinear previsions, and as a supremum of superlinear previsions under mild conditions. This extends to homeomorphisms between spaces of previsions and certain hyperspaces over spaces of sublinear or superlinear previsions, which can also be characterized in terms of orthogonality relations, making the construction a variant of a double powerspace construction.

翻译：预想是正齐次泛函，也是积分泛函的推广形式。我们研究预想——仅针对预想本身，而非先前工作中涉及的子线性或超线性预想。我们证明：在温和条件下，每个预想可表示为子线性预想的下确界，也可表示为超线性预想的上确界。这一结论可推广至预想空间与子线性/超线性预想空间上特定超空间之间的同胚关系，该关系还可通过正交性刻画，从而将该构造转化为双重幂空间构造的变体。