2744 INDEX

locally compact , 167locally convex topological vector space, 479locally finite, 421, 1023, 1253logarithm

branch of logarithm, 1653lower semicontinuous, 487

equivalent conditions, 908Lusin’s theorem, 416Lyapunov Schmidt procedure, 735

manifold, 1257manifolds

boundary, 1061interior, 1061orientable, 1063radon measure, 1259smooth, 1063surface measure, 1259

mappingcompact, 790

Marcinkiewicz interpolation, 1121martingale, 1948

quadratic variation, 2121martingales

equiintegrable, 2105matrix

left inverse, 76lower triangular, 77non defective, 90normal, 90right inverse, 76upper triangular, 77

maximal chain, 2725maximal function

Radon measures, 1081maximal monotone

approximation, 896, 2646coercive, 893equivalent conditions, 880evolution inclusion, 1374interior of domain, 884linear map, 927onto, 892pseudomonotone, 887subgradient, 911

sum of two of them, 902, 904sum with duality map, 881sum with monotone and hemicontinu-

ous, 902maximal monotone

Banach space, 868maximal monotone operator, 1367

sum with a subgradient, 919maximum modulus theorem, 1655McShane’s lemma, 623mean ergodic theorem, 494mean value inequality, 120, 716, 731mean value theorem, 716, 731

for integrals, 58measurable, 269

Borel, 226multifunctions, 1533, 2391

measurable function, 226pointwise limits, 226

measurable functionsBorel, 234combinations, 231

measurable rectangle, 321, 397measurable representative, 677measurable selection, 1534, 1536, 2392

from set of limits, 1578measurable selection theorem, 2597

improved version, 2603limits of measurable functions, 2603

measurable sets, 223, 269measure

σ finite, 261inner regular, 259outer regular, 259

measure space, 223isomorphic, 1527regular, 407separable, 1527

measuresregularity, 259

Mellin transformations, 1691meromorphic, 1638Merten’s theorem, 1768metric, 137

properties, 137