Stieltjes measure
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1: 1.1 Special Notation
$x,y$  real variables. 

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${L}^{2}(X,d\alpha )$  the space of all Lebesgue–Stieltjes measurable functions on $X$ which are square integrable with respect to $d\alpha $. 
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2: 1.4 Calculus of One Variable
Absolutely Continuous Stieltjes Measure
… ► … ►Stieltjes Measure with $\alpha (x)$ Discontinuous
… ► See Riesz and Sz.Nagy (1990, Ch. 3). … ►Definite integrals over the Stieltjes measure $d\alpha (x)$ could represent a sum, an integral, or a combination of the two. …3: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
4: 18.2 General Orthogonal Polynomials
5: 1.16 Distributions
6: 18.39 Applications in the Physical Sciences
7: Errata
The following additions were made in Chapter 1:

Section 1.2
New subsections, 1.2(v) Matrices, Vectors, Scalar Products, and Norms and 1.2(vi) Square Matrices, with Equations (1.2.27)–(1.2.77).

Section 1.3
The title of this section was changed from “Determinants” to “Determinants, Linear Operators, and Spectral Expansions”. An extra paragraph just below (1.3.7). New subsection, 1.3(iv) Matrices as Linear Operators, with Equations (1.3.20), (1.3.21).
 Section 1.4

Section 1.8
In Subsection 1.8(i), the title of the paragraph “Bessel’s Inequality” was changed to “Parseval’s Formula”. We give the relation between the real and the complex coefficients, and include more general versions of Parseval’s Formula, Equations (1.8.6_1), (1.8.6_2). The title of Subsection 1.8(iv) was changed from “Transformations” to “Poisson’s Summation Formula”, and we added an extra remark just below (1.8.14).

Section 1.10
New subsection, 1.10(xi) Generating Functions, with Equations (1.10.26)–(1.10.29).

Section 1.13
New subsection, 1.13(viii) Eigenvalues and Eigenfunctions: SturmLiouville and Liouville forms, with Equations (1.13.26)–(1.13.31).

Section 1.14(i)
Another form of Parseval’s formula, (1.14.7_5).

Section 1.16
We include several extra remarks and Equations (1.16.3_5), (1.16.9_5). New subsection, 1.16(ix) References for Section 1.16.

Section 1.17
Two extra paragraphs in Subsection 1.17(ii) Integral Representations, with Equations (1.17.12_1), (1.17.12_2); Subsection 1.17(iv) Mathematical Definitions is almost completely rewritten.

Section 1.18
An entire new section, 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions, including new subsections, 1.18(i)–1.18(x), and several equations, (1.18.1)–(1.18.71).