Spaces of measurable transformations

Spaces of Measurable Transformations

By a space we shall mean a measurable space, i.e. an abstract set together with a <r-ring of subsets, called measurable sets, whose union is the whole space. The structure of a space will be the <r-ring of its measurable subsets. A measurable transformation from one space to another is a mapping such that the inverse image of every measurable set is measurable. Let X and F be spaces, F a set of...

Measurable Transformations

A Universal Integral Independent of Measurable Spaces and Function Spaces

For [0,∞]-valued (monotone) measures and functions, universal integrals are introduced and investigated. For a fixed pseudomultiplication ⊗ on [0,∞] the smallest and the greatest universal integrals are given. Finally, a third construction method for obtaining universal integrals is introduced.

Lecture 1 Measurable Spaces Families of Sets

Families of Sets Definition 1.1 (Order properties). A countable1 family {An}n∈N of 1 To make sure we are all on the same page, let us fix some notation and terminology: • ⊆ denotes a subset (not necessarily proper). • A set A is said to be countable if there exists an injection (one-to-one mapping) from A into N. Note that finite sets are also countable. Sets which are not countable are called ...

Diagonal operators on spaces of measurable functions

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