Linear approximations in convex metric spaces & the application in the mixture theory of probability theory Book

	Introduction	1
I	Linear approximation in convex metric spaces	5
1	Convex metric spaces	5
1.1	Convex spaces	6
1.2	Convex metric spaces	8
2	Decomposability in totally convex metric spaces	14
2.1	Integration in totally convex metric spaces	14
2.2	Decomposability of elements of a totally convex metric space	16
3	Special cases	20
3.1	The set of weight functions is the set of discrete probability distribution functions with jumps at finitely many prescribed points	20
3.2	The set of weight functions is the set of discrete probability distribution functions with jumps at infinitely many prescribed points	23
3.3	The set of weight functions is the set of absolutely continuous probability distribution functions with square integrable density function	29
II	Decomposability of distribution functions	35
4	Formulation of the problem	35
5	Decomposability of distribution functions	49
5.1	Considerations on the set of all probability distribution functions	50
5.2	Considerations on the set of probability distribution functions concentrated on a finite or infinite interval	63
5.3	Considerations on the set of continuous probability distribution functions	70
5.4	Considerations on the set of discrete probability distribution functions	84
	App. A Two theorems on mixtures of probability distribution functions	97
	App. B Totally positive matrices. The transsignation of a matrix	100
	App. C The determinant theorem of Cauchy, with corollaries	101
	App. D A representation of two polynomials	105
	App. E Cauchy matrices of special type	107
	App. F On a matrix identity	110
	App. G Solution of a matrix equation. On an extension of the Sherman-Morrison theorem	112
	App. H The moment problem of Hamburger. On the solution of the full moment problem of Stieltjes	116
	App. J Integration by parts for Stieltjes integrals	123
	References and bibliography	129
	Index	132