Real Analysis

Gerald B. Folland, R. A. M. T., & Their Applications, 2. e. (1999). Real Analysis: Modern Techniques and Their Applications. Wiley.

Type

Book chapter

Intellectual base

Textbook

Year

1999

ISBN

9780471317166

Link

https://openlibrary.org/books/OL375390Mmatched

Cited by

6 citations across 6 artifacts.

Domain-specific

• Complete field
  • The entry centers metrizable valued fields and sequence completeness; uniform-space, topological-field, higher-rank valuation, and spherical-completeness variants require their own convergence conventions.
• Local boundedness
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Product measure
  • A product measure \(\mu\otimes\nu\) is a measure on \(\mathcal A\otimes\mathcal B\) satisfying \((\mu\otimes\nu)(A\times B)=\mu(A)\nu(B)\) for measurable rectangles, with the usual convention for zero times infinity.
• Space of continuous functions on a compact space
  • The identity is the full scalar-valued C(X) algebra on compact Hausdorff X; noncompact domains, vector-valued codomains, and proper function subalgebras require separately declared variants.
• Trivial measure
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Vague topology
  • The vague topology is the weakest topology on a space of Radon measures for which every map taking a measure to its integral against each permitted test function is continuous.

Verification

This reference passed the adversarial substantiation pipeline: it was checked to exist and to support the claim it is attached to. See how references were verified.

Registry ID ref:c7694c6af6d0 · see in the full table