I - Introduction
Review articleOpen access

Publisher SummaryThis chapter discusses the basic notions and results from real and complex function theories and probability theory. It discusses the Fubini–Tonelli theorem, Lebesgue decomposition theorem, Jensen's theorems, Carleman's theorems, maximum modulus theorem, and theorems of Phragmen–Lindelöf. The notion of a function of bounded variation is generalized to multidimensional functions. A nondecreasing function is equivalent to the assignment of a measure, and the total variation of a function of bounded variation is an additive interval function. A linear operator is bounded if and only if it is uniformly continuous, and it is uniformly continuous if and only if it is continuous at an element.

Request full text

References (0)

Cited By (0)

No reference data.
No citation data.
Join Copernicus Academic and get access to over 12 million papers authored by 7+ million academics.
Join for free!