Real Analysis

Folland, G. B. (1999). Real Analysis: Modern Techniques and Their Applications. Wiley.

Type

Book

Intellectual base

Textbook

Year

1999

Pages cited

1-2

ISBN

9780471317166

Link

https://www.wiley-vch.de/en/areas-interest/mathematics-statistics/real-analysis-978-0-471-31716-6

Cited by

12 citations across 12 artifacts.

Each citation links to the sentence it supports in the citing article.

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.
• Mean of a function
  • … constitutive identity and a convenient observable transfers from A canonical example satisfies the full defining rule of Mean of a function with assumptions and conventions explicit. to A careful use of Mean of a function tests the constitutive rule and nearest confusable rather than relying on the label alone..
• Measure space
  • Completion may enlarge \(\Sigma\) by adding subsets of null sets, so two measure spaces can share \(X\) and the same numerical rule on a smaller family yet differ in measurable structure.
• Null Set
  • In a complete measure space, every subset of a null measurable set is measurable and null; completing a measure adds precisely the subsets needed for that closure.
• Pre-measure
  • … constitutive identity and a convenient observable transfers from A canonical example satisfies the full defining rule of Pre-measure with every parameter and convention explicit. to A careful use of Pre-measure tests its carrier, assumptions, boundary and nearest confusable rather than relying on the label alone..
• 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.
• Riesz–Markov–Kakutani representation theorem
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• 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.

Mechanisms

• Null-Set Policy Register
  • The distinction it enforces is real: a null set can be nonempty and even large in every sense but measure.

    This sourceDefines null sets by zero measure, a condition that does not require the set to be empty.

Verification

Does it exist? Confirmed. This work's ISBN resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Not recorded. Neither this nor any other of the 12 citations of this work carries a recorded support check.

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Registry ID ref:d7dabbb16298 · see in the full table