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Ruziewicz problem

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22: 51: 181: 73: 44: 34: 38: 30: 302: 55: 156: 280: 241: 212: 8: 122: 169: 177: 145: 114: 271: 287: 266: 229: 133: 103: 276: 253:> 3 there is only one finitely additive rotationally invariant measure on the 237: 208: 137: 99: 296: 87: 233: 176:, Progress in Mathematics, vol. 125, Basel: Birkhäuser Verlag, 113:
is characterised, up to proportionality, by its properties of being
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Margulis, Grigory (1980), "Some remarks on invariant means",
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Drinfeld, Vladimir (1984), "Finitely-additive measures on
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Discrete groups, expanding graphs and invariant measures
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This was answered affirmatively and independently for
294: 43:but its sources remain unclear because it lacks 259:Bulletin of the American Mathematical Society 257:-sphere on all Lebesgue measurable sets", 270: 74:Learn how and when to remove this message 248: 219: 199:, invariant with respect to rotations", 190: 168: 295: 15: 148:(published 1984). It fails for the 13: 14: 314: 20: 272:10.1090/S0273-0979-1981-14880-1 201:Funktsional. Anal. I Prilozhen. 249:Sullivan, Dennis (1981), "For 1: 162: 288:Survey of the area by Hee Oh 7: 155:The problem is named after 10: 319: 222:Monatshefte fĂĽr Mathematik 96:Banach–Ruziewicz problem 29:This article includes a 102:asks whether the usual 58:more precise citations. 140:around 1980, and for 121:, and defined on all 170:Lubotzky, Alexander 157:StanisĹ‚aw Ruziewicz 123:Lebesgue measurable 234:10.1007/BF01295368 117:, invariant under 31:list of references 146:Vladimir Drinfeld 115:finitely additive 92:Ruziewicz problem 84: 83: 76: 310: 283: 274: 244: 215: 186: 134:Grigory Margulis 104:Lebesgue measure 79: 72: 68: 65: 59: 54:this article by 45:inline citations 24: 23: 16: 318: 317: 313: 312: 311: 309: 308: 307: 293: 292: 184: 165: 138:Dennis Sullivan 80: 69: 63: 60: 49: 35:related reading 25: 21: 12: 11: 5: 316: 306: 305: 303:Measure theory 291: 290: 285: 265:(1): 121–123, 246: 228:(3): 233–235, 217: 188: 182: 164: 161: 100:measure theory 82: 81: 39:external links 28: 26: 19: 9: 6: 4: 3: 2: 315: 304: 301: 300: 298: 289: 286: 282: 278: 273: 268: 264: 260: 256: 252: 247: 243: 239: 235: 231: 227: 223: 218: 214: 210: 206: 202: 198: 194: 189: 185: 183:0-8176-5075-X 179: 175: 171: 167: 166: 160: 158: 153: 151: 147: 144:= 2 and 3 by 143: 139: 135: 131: 126: 124: 120: 116: 112: 110: 105: 101: 97: 93: 89: 78: 75: 67: 57: 53: 47: 46: 40: 36: 32: 27: 18: 17: 262: 258: 254: 250: 225: 221: 204: 200: 196: 192: 173: 154: 141: 129: 127: 108: 95: 91: 85: 70: 61: 50:Please help 42: 94:(sometimes 88:mathematics 56:introducing 163:References 207:(3): 77, 119:rotations 64:July 2024 297:Category 172:(1994), 281:0590825 242:0596890 213:0757256 132:≥ 4 by 125:sets. 111:-sphere 106:on the 52:improve 279:  240:  211:  180:  150:circle 90:, the 98:) in 37:, or 195:and 178:ISBN 136:and 267:doi 230:doi 86:In 299:: 277:MR 275:, 261:, 238:MR 236:, 226:90 224:, 209:MR 205:18 203:, 159:. 152:. 41:, 33:, 284:. 269:: 263:4 255:n 251:n 245:. 232:: 216:. 197:S 193:S 187:. 142:n 130:n 109:n 77:) 71:( 66:) 62:( 48:.

Index

list of references
related reading
external links
inline citations
improve
introducing
Learn how and when to remove this message
mathematics
measure theory
Lebesgue measure
n-sphere
finitely additive
rotations
Lebesgue measurable
Grigory Margulis
Dennis Sullivan
Vladimir Drinfeld
circle
Stanisław Ruziewicz
Lubotzky, Alexander
ISBN
0-8176-5075-X
MR
0757256
doi
10.1007/BF01295368
MR
0596890
doi
10.1090/S0273-0979-1981-14880-1

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