All Superinterfaces:: GeneralizedMetricVectorSpace, GeneralizedVector, R1GeneralizedVector

All Known Implementing Classes:: R1Combinatorial, R1CombinatorialBall, R1Continuous, R1ContinuousBall

public interface R1Normed
extends GeneralizedMetricVectorSpace, R1GeneralizedVector

R1Normed Abstract Class implements the Normed, Bounded/Unbounded Continuous/Combinatorial l_p R^d Spaces. The Reference we've used is:

Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators Cambridge University Press Cambridge UK

It provides the following Functionality:

Retrieve the Borel Sigma R¹ Probability Measure
Compute the Metric Norm of the Sample
Retrieve the Population Mode
Compute the Borel Measure Expectation for the specified R¹ To R¹ Function over the full Input Space

Module	Computational Core Module
Library	Statistical Learning Library
Project	R¹ and R^d Vector/Tensor Spaces (Validated and/or Normed), and Function Classes
Package	Hilbert/Banach Normed Metric Spaces

Field Summary

Fields inherited from interface org.drip.spaces.metric.GeneralizedMetricVectorSpace
EUCLIDEAN_NORM, L2_NORM, LINFINITITY_NORM

Method Summary

Modifier and Type	Method	Description
`double`	`borelMeasureSpaceExpectation(R1ToR1 r1ToR1Function)`	Compute the Borel Measure Expectation for the specified R¹ To R¹ Function over the full Input Space
`R1Univariate`	`borelSigmaMeasure()`	Retrieve the Borel Sigma R¹ Probability Measure
`double`	`populationMode()`	Retrieve the Population Mode
`double`	`sampleMetricNorm(double x)`	Compute the Metric Norm of the Sample

pNorm, populationMetricNorm

cardinality, hyperVolume, isPredictorBounded, leftEdge, match, rightEdge, subset

validateInstance

Interface R1Normed