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1. Basic presentation of the integral
In the following, F is a real or complex vector space of finite dimension (denoted, where appropriate, by p). When F = , it is denoted F = K. The space F is provided with any norm ││ · ││; the norm equivalence theorem ensures that the results obtained do not depend on the particular norm chosen. In the case of K, either the absolute value or the modulus is used.
1.1 Constructing the integral of a controlled application
In this paragraph, we consider a segment [a, b], with a < b.
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Basic presentation of the integral
Lebesgue integral
