INDEX 2745

metric space, 135, 137Cauchy sequence, 135closed set, 135compact, 143compactness of product space, 148complete, 140completely separable, 142conditions for compactness, 144distance to a set, 136distance to set is continuous, 136extreme value theorem, 147limit points, 135open balls open, 135open set, 135, 137separable, 142sequentially compact, 143Tietae extension, 156uniform continuity, 147uniform continuity on compact set, 147

Meyer Serrin theorem, 1267Mihlin’s theorem, 1135min max theorem, 871Minkowski functional, 475, 483Minkowski inequality, 401

integrals, 404Minkowski inequality

backwards, 451Minkowski’s inequality, 404minor, 74Mittag Leffler, 1695, 1795mixed partial derivatives, 125, 725modification, 2049modular function, 1831, 1833modular group, 1765, 1822module of periods, 1818mollifier, 412monotone, 824, 2525monotone , 868

Banach space, 868monotone and hemicontinuous

coercive, 882monotone class, 320monotone convergence theorem, 245monotone graph extended, 877monotone operators , 868

monotone set valuedvariational inequality, 874

Montel’s theorem, 1741, 1761Moreau’s theorem, 915, 1395Morrey’s inequality, 956, 1238mountain pass theorem

Banach space, 821Hilbert space, 810

multi-index, 100, 125, 195, 1097multifunctions, 1533, 2391

measurability, 1533, 2391multipliers, 1124Muntz’s first theorem, 533Muntz’s second theorem, 534

natural, 2151, 2154Nemytskii operator, 1579Neuman series, 728Neumann series, 1699no retract onto boundary of ball, 772non equal mixed partials

example, 726norm

p norm, 186normal, 1910, 1932, 2006normal family of functions, 1742normal filtration, 2060normal topological space, 165Normed linear space, 186not pseudomonotone, 825nowhere differentiable functions, 473nuclear operator, 551numerical range, 1712

obstacle problemnon-constant obstacle, 1571

one point compactification, 167, 284open ball, 137

open set, 137open cover, 143, 167open mapping theorem, 439, 1651open set, 97, 137open sets, 164

countable basis, 142operator norm, 114, 437