Definition of "pseudometrics"

Given T ⊂ R {\displaystyle T\subset \mathbb {R} } and a metric space M {\displaystyle M} , we introduce a nondecreasing sequence of pseudometrics { ν n } {\displaystyle \{\nu _{n}\}} on M T {\displaystyle M^{T}} (the set of all functions from T {\displaystyle T} into M {\displaystyle M} ), called the joint modulus of variation.

2016, Vyacheslav V. Chistyakov, Svetlana A. Chistyakova, “The joint modulus of variation of metric space valued functions and pointwise selection principles”, in arXiv‎