β Scribed by Marek Balcerzak; Tomasz Filipczak
No coin nor oath required. For personal study only.
We extend results of Elekes and MΓ‘thΓ© on monotone Borel hulls to an abstract setting of measurable space with negligibles. This scheme yields the respective theorems in the case of category and in the cases associated with the Mendez Ο-ideals on the plane.
π SIMILAR VOLUMES
This paper deals with monotonic binary operations F : [0; 1] 2 β [0; 1] with the property (called locally internal property) that the value at any point (x; y) is always one of its arguments x; y. After stating a theorem that characterizes this kind of operations, some special cases are studied in d
We provide sufficient conditions for a sequence of positive linear approximation operators, L n ( f, x), converging to f (x) from above to imply the convexity of f. We show that, for the convolution operators of Feller type, K n ( f, x), generated by a sequence of iid random variables taking values