If A(f) =-A, p(^; u, u') == I u' \ u' (so that (3 depends only on u'), the equation represents a classical vibrating membrane with the resistance proportional to the velocity ( 2 ).We shall give some sufficient conditions on A(t) and on ^(t; u, u') so that (i), together with the initial conditionsis a well-posed problem, i. e., so that there exists a unique solution in the whole interval [o, T]; of course this implies corresponding results on a half-line [o, oo). For some quite general local results, we refer to LERAY [8], DIONNE [5] and SOBOLEVSKIJ [20].We shall also briefly consider first-order evolution equations of the type (3) A(Q u(t) + u'(t) + (3(/; u(0) = f(t\( 3 ) T. KATO [27] has another kind of extension by a different method.

Dealing with a problem posed by Kupka we give results concerning the permanence of the almost strong lifting property (respectively of the universal strong lifting property) under finite and countable products of topological probability spaces. As a basis we prove a theorem on the existence of liftings compatible with products for general probability spaces, and in addition we use this theorem for discussing finite products of lifting topologies.

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Product liftings and densities with lifting invariant and density invariant sections by K. M u s i a l (Wroc law), W. S t r a u s s (Stuttgart) and N. D. M a c h e r a s (Piraeus)