Table Of Contents:
Preface vii

Lipschitz Spaces 1(32)

Metric spaces 1(2)

Lipschitz functions 3(3)

Products of metric spaces 6(3)

Quotients of metric spaces 9(4)

Scalar-valued Lipschitz functions 13(6)

Lipschitz spaces 19(5)

Lip and Lip0 24(4)

Composition maps 28(2)

Notes 30(3)

The Predual 33(40)

De Leeuw's map 33(5)

The Arens-Eells space 38(5)

The mass transfer problem 43(6)

Weak* extreme points (existence) 49(5)

Weak* extreme points (characterization) 54(7)

Isometries of Lip spaces 61(6)

Isometries of Lip0 spaces 67(3)

Notes 70(3)

Little Lipschitz Spaces 73(28)

lip0(X) 73(4)

Extensions of little Lipschitz functions 77(5)

Double duality 82(4)

Cubes in RN 86(6)

Compact subsets of RN 92(7)

Notes 99(2)

Lipschitz Algebras 101(36)

Order complete subalgebras 101(6)

Order complete ideals 107(5)

Carrier spaces 112(5)

Little Lipschitz subalgebras 117(6)

Little Lipschitz ideals 123(2)

Norm closed ideals 125(3)

Point derivations 128(2)

Spectral synthesis 130(6)

Notes 136(1)

Lipschitz Lattices 137(24)

Stone lattices 137(3)

Completely distributive lattices 140(3)

Raney's theorem 143(3)

Lip(X) as a vector lattice 146(4)

Lipschitz lattices, I 150(3)

Lipschitz lattices, II 153(6)

Notes 159(2)

Measurable Lipschitz Algebras 161(28)

Measurable metrics 161(7)

Lip(X,μ), I 168(8)

Lip(X,μ), II 176(5)

Measurable Lipschitz lattices 181(6)

Notes 187(2)

Derivations 189(24)

Examples 189(8)

The derivation theorem 197(4)

The exterior derivative 201(5)

Noncommutative metrics 206(4)

Notes 210(3)
Table of Symbols 213(2)
Bibliography 215(6)
Index 221