mathlib documentation

measure_theory.measure.complex

Complex measure #

This file proves some elementary results about complex measures. In particular, we prove that a complex measure is always in the form s + it where s and t are signed measures.

The complex measure is defined to be vector measure over , this definition can be found in measure_theory.measure.vector_measure and is known as measure_theory.complex_measure.

Main definitions #

Tags #

Complex measure

Given s and t signed measures, s + it is a complex measure

Equations

The complex measures form an equivalence to the type of pairs of signed measures.

Equations
@[simp]