Talk:Bernstein's theorem on monotone functions

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Definition too restrictive?

Is the statement correct? My gut feeling (without any experience of the theorem) is that cumulative probability distribution function is too restrictive; rather it should be with respect to a cumulative distribution function of a positive measure whose total measure is positive and finite, but not necessarily equal to 1? Dmharvey 19:55, 15 February 2006 (UTC)[reply]

I think you're right. I'll be back.... Michael Hardy 22:08, 15 February 2006 (UTC)[reply]

Just checking - do you guys think that Bernstein's theorem on the existence and uniqueness of solutions of the equation d2y/dx2 = H(x,y,y') y(a)=A, y(b)=B should also be mentioned here. I'm not an experienced mathematician - but in the subject of calculus of variations, for example, it seems that "Bernstein's theorem" would be more likely to refer to this existence theorem.