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Content available remote Majorizing Measures and Ultrametric Spaces
EN
Talagrand's proof of the sufficiency of existence of a majorizing measure for the sample boundedness of processes with bounded increments used a contraction from a certain ultrametric space. We give a short proof of existence of such an ultrametric using admissible sequences of nets.
EN
We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded increments.
3
Content available remote A note on the Men'shov-Rademacher inequality
EN
We improve the constants in the Men'shov-Rademacher inequality by showing that for n > 64, E[...) for all orthogonal random variables X1,..., Xn such that ∑[...]= 1.
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